Fire Emblem: Three Houses
tl;dr version:
Detailed ratings:
Mostly rating on a "1 is the worst, 10 is the best" scale rather than worrying what a 10 is compared to other games.
In general, the optimum path for physical characters is (any beginner class) -> Brigand/Pegasus Knight -> Wyvern. Everyone can take it, and while talent list matters it's never a deal-breaker. I'll mention other roles sometimes but that's generally the baseline for a character's performance, even though in practice you will probably send some people to other classes just for weapon/battalion variety reasons. Magic users have an assumed default path of Monk -> Mage -> Warlock, with an optional finish in Dark Knight or Gremory.
I'm not factoring in paid DLC for this, outside the characters who only exist with it.
Byleth: 8.5/10. Has the same stupid base stats and accelerate exp as Edelgard, but lower str growth, worse talent list, and no Raging Storm. The (bad) wildcard is his/her training method; assuming 2/3 instruct rate everyone else gets +70 skill exp per weak if training neutral things on Maddening, while Byleth needs 3.5 explore actions to keep up, which is rough. Later on it's not a big deal though, so the great stats do shine through.
Edelgard: 10/10. The only real concern here is the speed is merely "decent" but a lot of things prop it up in practice (str, Weight-3, her exp bonus, Darting Blow). The overall stats (str/cha in particular) and talent list are outstanding, and Raging Storm is kinda insane. 15 uses of "take an extra turn" pretty much cement her as the best character in the game on her own route, and... probably overall too.
Hubert: 5/10. He's okay. He has solid stats, gets 3 range spells, and his Frozen Lance hits pretty hard once he closes to melee. A trash faith list combined with the fact that there's no way for him to have both good move and his spells until Level 30 hurts, though.
Dorothea: 8/10. Thoron, Physic, Meteor is quite a combo. The magic stat is less good, but since it's all in the growth instead of the base it's not as bad as it could be.
Ferdinand: 6/10. A bit of a slow start with his bases (and truthfully his stats never stand out), but his personal makes him one of the best dodge-tanks. Swift Strikes is kinda cool too, though brave weapons are available soon enough after reaching A ranks that I don't care that much.
Bernadetta: 4.5/10. Bernie has bad stats (bases, growths, you name it) and a bad talent list, but is saved by a neat personal skill which props up her damage and some cool combat arts like Vengeance and Encloser. It's enough you probably do want to train her in bows/lances whatever class you send her (some combination of pegasus and archer classes is probably best).
Caspar: 3/10. Probably the worst of the 24 students, he doesn't have much going for him. His personal's decent, but his stats are poor (even his strength doesn't really stand out, it's Petra with +5% growth or Ferdie with +1 base) and he did not need an authority bane on top of that.
Petra: 7.5/10. There's a lot to like here: axe/flying talent, great speed (combos with flying talent to make her a great dodge-tank candidate) and adequate str. Doesn't really go the extra mile by having better charm/durability and her personal skill is kinda worthless, but she's obviously good.
Linhardt: 6/10. He has Physic and Warp, and the magic stat to use them. He also has the worst combat stats of the mages, though Wind makes his speed less terrible than it first appears (still bad). So he's behind the likes of Dorothea and Marianne, but still a solid choice.
Dimitri: 9.5/10. Well Edelgard is the obvious comparison: he's slightly ahead on stats overall though has a worse start, has no pegasus, won't train for four chapters, and no Raging Storm. That said most of the good stuff otherwise applies to him, and he has Battalion Vantage/Wrath which is a mean combo that lets him pull off unique things.
Dedue: 5.5/10. Probably shouldn't be used in the second half of the game (though you can, and if you're gonna set up anyone for raw def in the second half it's gonna be him) but he's very solid in the first half, with enough def (thanks to his personal) that even I take notice, and good str/Vengeance to output some strong part 1 offence.
Felix: 7.5/10. In that conversation for "best non-lord physical student". Out of the people in the running for that, he has the best stats (10 str/9 spd and 55% growth in both) but the worst talent list (authority bane in particular). Great start on his own route thanks to his personal, which is nice.
Mercedes: 8/10. Would be basically perfect if she had 3 range. Her stats are a cut above most mages (actually has 8 base spd, solid def/res/charm), and Physic + Fortify is great. Her personal and statline both encourage you to frontline her then heal herself as she heals others which is neat for action economy.
Ashe: 4/10. He's somewhat speedy and having both axe+bow talents is nice whichever route you end up going with him. His personal is more convenient than objectively useful, but it's there. The rest of the stat build doesn't really do him favours but it's workable. Deadeye has some niche use. Probably a little worse than Bernie.
Annette: 4/10. Her spell list is just depressing, and it's not like her stats make up for it or anything (in fact, they're pretty subpar too tbh). She does have a solid Rally (Str from her personal, gets Spd pretty fast) and an authority boon, and can do some decent stuff with magical axes (Bolt Axe, Lightning Axe, her relic) later in the game, but this isn't really an optimum plan for a 3H mage.
Sylvain: 7/10. Just quietly solid. See Ferdinand if his personal helped more early (extra str/def in some situations) and less late (due to not scaling), but he also gets Ruined Sky (35 might!) in Chapter
6 so that's a thing. Also has a very legit mage build if that's your thing.
Ingrid: 7/10. I've generally been convinced that Sylvain is slightly better, but they're close. A shaky start but she grows into "slightly worse Petra" nicely, and you can even quibble if she's worse midgame due to Burning Quake.
Claude: 9/10. He's perhaps easiest to compare with Felix: after factoring in his level boost he has basically the same speed and falls off in str late, but has way more charm and his skill/talent situation is amazing instead of bad: +authority, +axe, +flying, +riding (Move+1), gets handed great Advanced/Master tier jobs for free. It'd be nice if his str were a bit higher or he had pegasus but otherwise you can scarcely ask for more.
Lorenz: 3.5/10. Lorenz has the stat build to be an interesting if not overwhelming mage (solid bulk), but unfortunately his spell list is trash (outside getting Ragnarok a bit early) which means he's not really very good as one anyway. He's a vaguely okay Paladin with Frozen Lance but you can do better.
Hilda: 7/10. She's a lot like Sylvain. She gets access to pegasus/Darting Blow (and has marginally better stats), but has an authority bane and gets her delete-button relic six chapters later. It roughly balances.
Raphael: 3.5/10. In his favour: pretty good str and that's a very important stat in this game. Not in his favour: 6+15% speed is game-worst among students. That's a big weakness and I feel like his str needed to be better than Felix-level in order to justify it on someone who doesn't have much else to recommend him.
Lysithea: 7/10. She's possibly a bit better if you factor DLC since one of her problems is tier 3 kneecapping her magic advantage. Otherwise, she's the best mage at nuking things (both the stat and the spell list, particularly Luna) and Mastermind helps get her get some skills faster, but is light on utility (Warp's nice, I prefer Physic though) for the stronger mages in the game.
Ignatz: 3.5/10. Having 8+35% / 8+50% offence with no personal to boost it is pretty bad. His talent list makes him an awful wyvern (relatively) and as an archer I'm not impressed by his list of combat arts (at least Ashe has Deadeye).
Marianne: 7/10. Compared to other mages, her biggest problem is being only neutral Reason, which makes certifying for Warlock on time rough. Like Lys she's a bit better with DLC because she certifies for the DLC mage classes more easily. Otherwise, has Thoron and Physic, so is Dorothea with a bit more magic but worse talents and no Meteor, which is a losing trade but still leaves her a great unit.
Leonie: 7.5/10. Petra remix. She doesn't get Alert Stance as easily (+lance not as good as +axe/flying for the game both want to play) but in exchange she's got better def/charm (i.e. just an outstanding overall stat build) and a non-trash personal. This probably roughly balances.
From here on we hit the staff members. To avoid repeating myself: joining late in this game means missing out on a bunch of skills or needing to backtrack to get them, and that kinda sucks.
Seteth: 6/10. Is Sylvain with no Ruined Sky but generally better stats... except speed which is rough. This might be a winning trade except that he joins in Chapter 12, which means he either sucks for a few maps or loses Atk to Sylvain as well. So obviously worse than Sylvain, but still a respectable unit, the best of the later-joining (post-Chapter 6) PCs.
Flayn: 3/10. Her thing is Rescue, and later Fortify, but joining with E reason means her offence is wretched and her utility is too situational. Really needed to either auto-train Reason or have Physic.
Hanneman: 4/10. His reason kit could hardly be better with Meteor (at A+, admittedly) and Thoron, and hey there are other mages who can't double and have durability woes so his wretched speed is maybe... not as bad as it could be? Still bad though. Needing to wait until chapter 8 to start building faith and needing to wait on Warlock a bit while getting Fiendish Blow are both negatives he didn't need. Probably ends up around Annette level.
Manuela: 3.5/10. Honestly mage Manuela is problematic, though yes there's Warp (off bad magic) and Bolting (have fun training for it). As a fighter she's basically Ingrid (dat speed) except she joins in chapter 8 with questionable training. She can play a variety of roles but struggles to find much to excel in.
Gilbert: 1/10. You will notice that I haven't handed out any 2's, this is because Gilbert really is that much worse than the next worst unit in Three Houses. Seteth, if Seteth had way less speed/charm and had done way less training before he joined (E flying, D+ authority), oh and joins even later of course. Even his def isn't anything incredible. It'd be trivial to build an armour who is completely superior to base Gilbert by chapter 13, and you wouldn't because that character would be bad too.
Alois: 4/10. Joins a chapter earlier than Seteth (which probably also means 2 extra paralogues), so does have a bit more time to backtrack to Brigand and badly wants to because otherwise he's just a bulkier Caspar who hasn't trained flying yet. Once you do that his atk/def are solid at least (thanks to NPC Warrior growths), and his speed can be patched some by wyvern + the growth being okay instead of bad. Has a decent rally too, which is something. Still, needing catching up to be "decent" isn't a great place to be.
Catherine: 8/10. You want to recruit her ASAP, chapter 4 is possible but tricky; chapter 5 is easy if you know what you're doing though. I'm rating her based off that. Compared to Felix she misses out on early correction to her skill priorities, but her str/speed are even better (and she actually has good def), she gets pegasus, she doesn't have an authority bane, and if you do need her to earlygame nuke as a swordmaster she can. It adds up to the best non-lord physical character in the game, I think.
Shamir: 6/10. If you get her in Chapter 6 she has Felix-level str and average speed, and can nuke as a sniper if needed. She also gets Hunter's Volley early enough to have it for a notable length of time before everyone gets their hands on brave weapons. Unfortunately her good midgame is at odds with building her for later, and she's going to fall off in part 2. So similar to Dedue but she's more impressive at her best.
Cyril: 4.5/10. What if Petra/Leonie had trash bases and no pegasus knight access. He is saved somewhat by having Point-Blank Volley (and/or Vengeance) giving him some decent offence in part 1, and by part 2 his growths kick in so he's fine then, although always forever short of the characters I rate at 7 or higher who can do the same build better.
Jeritza: 7/10. Retribution means that the Death Knight mastery isn't as good as it sounds. But he has great stats (comparable to Catherine except he actually has res), gets Darting Blow in Chapter 14, and having a super version of the Paladin class gives you another canto badass without eating a flying battalion. Not really dominant because he does suffer from some usual latejoiner problems and is competing with Raging Storm, but he should slide into the team easily.
Yuri: 7/10. Great stats (Petra/Leonie trading HP for Res/Charm), authority boon, a decent personal (especially for a wyvern)... there's a lot to like here. Unfortunately his talent list is a bit of a mess and his stat build really does want Darting Blow to seal the deal.
Balthus: 5.5/10. Raphael with a few more points of speed (still sub-Caspar though), a relic (with an admittedly shaky combat art), and the big one, a rather potent personal. It doesn't add up to a great PC because speed's important (and flying bane doesn't help) but it's a respectable one.
Constance: 6/10. Her spell list is interesting with Rescue and Bolting, but no Physic or Thoron are downers. She invites comparison with Lysithea: same great magic and holes in her kit. She does get Bolting, which is definitely a big plus (lessened some by her short support list), but otherwise loses the comparison (Warp > Rescue, is only neutral faith, no Luna or Mastermind).
Hapi: 7/10. Nice spell list, with Physic, Warp (although faith neutral means she takes the longest to get it), and a range 3 spell (though at B). That said, just as Constance invites comparison to Lys, Hapi invites comparison to Dorothea, who has better stats (similar, but actually has charm), and an even better spell list (Meteor, Thoron is both better and earlier than Death).
Anna: unsure-but-bad/10. Manuela if she could start building relevant skills earlier but had worse stats and most importantly NO SUPPORTS which defeats part of the point of having Meteor, the most interesting thing about her. I've never used her and I can only guess at how much the "no supports" thing hurt. If she had a full support list she'd probably be around 4/10 though, which is not promising.