Max: 19
Lyon: 17

T.G. Nevareh
Well, let's see... Max versus Lyon, huh?

...Seriously?

Oh. Kay.

Well, let's see. Lyon and Max both come from the same kind of game. Let's look at those games, shall we?

Shining Force is a neat little package where Max and eleven friends can go and fight the same battle over and over again until they're strong enough to not to need to ever use any kind of strategy. People die pretty much all the time, but who cares when there's a handy priest at a nearby town who can just magic them back to life! There's no decent mechanic for weathering magic, which cannot miss, but is so limited in uses that a vast majority of everything anyone ever does is done by thwacking their opponents with their increasingly-oversized-and-shiny weapon of choice. Engagements are fought by walking towards your enemies and slaughtering them followed by picking money off of their corpses and using that money to resurrect your mages for the three-hundredth time. Your enemies are never far out of scale of your stats, so care isn't exactly something you need to take. And when you get a new sword made out of death and awesome, just pop it right on because it'll never wear out. Critical hits and dodging appear to work as a matter of faith, as we're all certain they occur, but damned if we'll ever figure out how or why.

Fire Emblem is a devastatingly calculating creature that lies in wait in even the most innocuous situations where you're given a vague idea what you're going up against and Heaven help you if you pick wrong from your too-large-yet-too-small party because if a unit is even mildly ill-suited for the mission it's probably dead. People die pretty much all the time unless very careful, and there's no way out of death once it happens. Magic works just the same as normal attacks, which means it can miss, throwing it into the intricate net of tactical possibilities already complicated by the fact that all of the best stuff breaks so easily it ends up unused and terrain that varies enough so paying attention to it matters. Money is found by various degrees of robbery and mercenary work. Enemies are usually -slightly- weaker than party members, rendering them only moderate threats, unless they're bosses in which case they're disproportionately strong and must be handled with great care. Critical hits and dodges are important and predictable enough to encompass the entire tactical niche occupied by several classes. Oh, and people in Fire Emblem ALWAYS counter-attack if they have a weapon.

Max is a protagonist; if he's hugely overleveled, he can take on big piles of enemies or even whole armies alone, though it's always advisable for him to have some kind of support or a healer to back him up, as he is a close-range dude with impressive physical defense and impressively lacking magical defense. Sure, once he gets in there he can tear stuff up.

Lyon is a boss in Fire Emblem with his own unique item for dealing death and is designed, like all Fire Emblem bosses, to require one of his weaknesses to be exploited in order for him to be taken down easily. Otherwise, he can wipe out entire teams with little effort. He also has the magic advantage of being able to attack at all close ranges- both one and two cells- allowing him to counterattack everything that isn't specifically long-range. Provided it's in range, he, being from Fire Emblem, will always counter-attack.

So Lyon can attack Max from a range that Max can't counter, and every time Max attacks Lyon, Lyon counterattacks. Lyon has some (I'll agree to not much) physical defense and Max has (depending on his iteration) next to none. Both of them have decent HP. Lyon's game has dodging built in as something you can rely upon to prevent damage and so Lyon can and will dodge every now and then, whereas Max's game includes dodging as a pleasant surprise. Lyon's weakness on the weapon triangle isn't something that Max can take effective advantage of
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Mechanically, Max has to be within one cell of Lyon to attack unless using his highly lackluster magic that Lyon's defenses will if not ignore than greatly reduce, and Lyon can attack from two cells away. Even if Max multi-attacks, Lyon will at least equal him blow-for-blow thanks to his counters and his attacks at range. And Lyon has a higher chance of critical damage and dodging.

Here's a better way to put it: Both are incomparable murder machines in their own right. However, Lyon is the one who comes from a game where being an incomparable murder machine actually requires some unique traits. In Shining Force (and especially the remake) everyone can be an incomparable murder machine. In Fire Emblem, we tend to worship those who can actually afford to ignore the tactical rules for a bit. And Lyon can ignore the rules.

Thomas vs Black Wizard