Dimitri
All the house leaders are exceptionally good. Dimitri is probably the most flawed of the three, but also has incredible upside.
The good: Well, let's start with the stats. Royal Lineage amps the already impressive numbers further, but even without considering that... 12+60% str is the best in the game (along with Edelgard), 9+55% charm trails only Edelgard, 7+40% def and 28+55% HP both trail only Dedue and Raphael... and unlike Dedue/Raphael, he actually has a good spd growth of 50%, though being male and having only 7 base prevents him from being actively good at this. This might well be the best overall stat build in the game. His talent list is a bit of a mix, but having +riding and +lance gives him easy access to mounted classes, and +authority is always great, essentially compensating for a bane elsewhere.
But of course, being a lord, he picks up some things post-timeskip that make him shine even more. First is his personal, which now grants him +20 avoid at full HP. See all the comments about dodgetank Ferdinand, Dimitri can do the same things but even better. (Dancer Dimitri is hilariously effective.) Second, his unique relic combat art, Atrocity. Unless his target has a Null Weakness ability, this lets Dimitri launch a 53-might attack, which kills almost anything in one hit. How good is this? Bernadetta or Dedue need to lose 37 HP just for their Silver Lance Vengeance to catch up, before considering Dimitri's superior strength. And Dimitri can do this at any time, with any HP. Finally, there's Battalion Vantage + Wrath. While maintaining battalion skills is a bit finnicky (you have to be careful to avoid damage which might finish the battalion off), it's hard to argue with the results: roughly 100% crit on enemy phase, with monstrous strength, allows him to finish off all but the tankiest enemies (e.g. monsters) before they can even strike him. And since he can do this with full HP (and his evade personal active), he's in far less danger than normal Vantage/Wrath builds. He also builds to it more easily, just needing A authority (which you would get for him anyway), instead of mastering two mediocre classes.
Dimitri can make a wide variety of builds work: paladin or high lord for maximal lance damage, super-str wyvern in the vein of Edelgard, battalion vantage/wrath (can stack with either of the previous), invincible dodgetank. The only consistent thing is he'll be an amazing unit regardless.
The less good: Though an outstanding unit, there are definitely some weaknesses worth noting. One is his bane in axes, which slows his path to the only male flying class. The other is the fact that he goes through a four-chapter stretch where he won't train at all, so it's extremely important you get the key parts of his build (e.g. A authority) up and running before then. And for a unit with a claim to be the best in the game, he's not super-impressive in the early stages (i.e. before level 20); in particular, a lack of pegasus knight means the best female physical units (e.g. FByleth, who also has better bases) will outclass him during that stage of the game.
That said he still has a claim to be the best unit in the game, for all that I personally think he falls just short. He's incredibly dominant post-timeskip; just as Edelgard is on CF, I think Dimitri is the unquestioned MVP for post-timeskip AM.
Dimitri's rating: 9.5/10
Use him?: Yes
Dedue
Dedue's got a great start and falls off a lot. FE3H doesn't use this model as much as earlier FEs due to how levels work, but it certainly sums up Dedue.
The good: As mentioned, he's got a good start. His HP/def are the best of anyone, his str not far behind (12, equal to Dimitri and one behind Edelgard/Byleth). But raw stats undersell how much better his def is than others, and that's because of his personal. Raising his def by 4 means it's actually 5 points higher than the next best, if he can afford to wait. Or, to put it another way to drive this home: the second best base defence in the game (7) is actually closer to Lysithea's (3) than it is to a waiting Dedue's (12). He can take hits nobody else can, and can dish back good damage too.
And once you train his lance rank up, his damage potential becomes even better. Vengeance allows him to deal out severe punishment if you can get his HP low: similiar to Bernie, except Dedue's got more HP to lose and more str (even after accounting for Persecution Complex, he passes Bernie at around Level 8). He doesn't get pegasus knight, but otherwise, he easily outclasses her at the use of this combat art.
He's got talent in axes and armour, so he can go wyvern easily, which also patches up his bad speed. Armour gives him Weight-3. Brawling gives him easy access to Grappler, and with his low speed and high str, he's a great fit for Fierce Iron Fist. One-Two Punch also helps out his punch damage before he masters Grappler, +8 damage at the cost of eating a counter in the middle, which is bad against mages, but good against physical units. On the axe side, he also gets Monster Breaker, which is solid (even aginst human enemies, it's the axe version of Tempest Lance). Whether by punching or with a brave axe, Dedue is ready to transfer away from using Vengeance when it falls off, and still have solid offence.
The less good: Dedue is let down by his speed growth and magic durability. At most points in the game, mages will typically double him for extreme (potentially even ORKO) damage, so any time mages are around (and from chapter 4 on, they're quite common compared to some other FEs), that puts a serious dent in his tanking game. He's -flying, which slows his path to wyvern, either putting him behind on skills (a problem which is exacerbated by what I'll talk about next) or consigns him to a low-mobility role which has to avoid mages.
He leaves from chapter 13 to 16, losing out on all training both in and out of battle. This tends to leave him somewhat unimpressive upon his return.
Finally, his tanking role is simply done much better by dodgetanks in this game, after the early going. He needs to avoid magic, dodgetanks do not. And concrete tanks require low-move classes to be at their most effective, while dodgetanks do best while flying.
Add that all up and there isn't much reason to use him once he returns, unless you like him. But he's outstanding for chapters 1-3, and decently solid for a while thereafter. I put more stock in performance after one is able to make party choices (i.e. recruitment starts) which hurts him a bit, but I still like him.
Dedue's rating: 5.5/10
Use him?: Yes early, but this drops to Maybe as the game goes on... he's a pretty good candidate to replace (and/or turn into a Dimitri adjutant) since you'll need a midgame replacement for him anyway.
Felix
Dedue's one candidate for best start of a non-lord student; Felix is the other. But Felix holds up better, for sure. On Hard I considered him the best non-lord student in the game; I don't think he still is on Maddening, but he's still great.
The good: 10+55% str, 9+55% speed. No other early joiner has that combination of str/spd for either bases or growths (though a few are lateral, like the lords, and Catherine matches/exceeds this once she shows up). At every point in the game, Felix hits hard and is one of the best at not being doubled, as well as above average at doubling things himself. None of his other stats are that special but they don't have to be, strength (or magic) and speed are far and away the two most important in this game. And the crazy thing is, those bases actually underrate his start, because his personal grants +5 damage without a battalion. Nobody has a battalion in chapter 1, and most people don't in chapter 2, so Felix essentially has 15 str + 9 spd to get started, which is just wild. It doesn't last long (even some low-rank battalions give better bonuses than +5 atk and nothing else, so you probably want to get him one in chapter 3 or at the latest, 4), but is still worth nooting.
With those stats, Felix will do well in any physical class, but I like to draw particular attention to his merits as an archer. He's +bows, and gets Heavy Draw, an underrated combat art, at C+. Bows often struggle to deal damage, since their only generic CA has only +1 damage. Heavy Draw provides +8, along with a hit boost, and lets him deal major damage against things he can't double, compared to other archers, who need to wait for Hunter's Volley to have anything that matches that. With his good speed for doubling, str for the brave bow, and Heavy Draw, he's a great choice for going bow knight while lesser archers have to stick with the less flexible sniper. Another notable CA he has is Nimble Combo, at Brawling C+, which similarly gives him a power advantage over his competition: +4 damage, also +20 avoid lets him null boss crit if they survive. And of course, if he doubles with gauntlets (or a brave weapon), that's 4 chances at +5 damage from his crest. And if none of those unique advantages appeal to you, he can always go wyvern, and excel as you would expect from anyone with his stat build.
The less good: The most damning thing about Felix by far is his authority bane; coupled with the fact that he doesn't actually have that many boons (he'd love axes, or riding, or flying, or armour), he's not actually in a great shape for training (and while not a factor for rating, this is even worse on non-BL routes, where he auto-trains the idiotic combo of swords+brawling). I often try to save the lord's battalion for him, since that only needs C, but that's a valuable tool and Felix's lowish charm (another weakness of his, at 5+30%) makes him less good at using it than I'd like. His other defensive stats aren't great either, similar to Petra, but like Petra, speed goes a long way towards helping me forgive that.
And as I've written before in comparisons with other units, he also can't get Darting Blow, which on Maddening is really important to maintain doubling ability long-term, meaning that he ends up a fair bit lower on the offensive speed ranking than 9+55% alone would suggest. Obviously this is a point in discussing any male physical unit but Felix's stat build craves it more than most.
Every house has a very solid fast physical unit (Petra and Leonie are the others); Felix certainly has the most flaws out of that trio, but sometimes it's hard to argue with his raw numbers, especially out of the gate.
Felix's rating: 7.5/10
Use him?: Yes (AM); Maybe (CF,VW,SS)