I've been playing it for a few days now - don't worry, I'm not going to mention any spoilers - and I would say that with this one they really went back to the drawing board. I'd say it definitely paid off. Now I know some people like Mekkah couldn't give a crap about the story and characters, that's the impression he gives anyway, but for people like me it'd be such a soulless experience if all there was to it was doing maths and placing little soldiers on the right tile. The series has always tried to characterise the units and contextualise the battles within a greater narrative. Traditionally, I think it's fair to say it was only mildly successful in that regard; the plots were clichéd and basic and so were the characters (9 and 10 might be exceptions, I haven't played them despite really wanting to but they do look very good in those regards).
Sure you might like those clichés, I certainly do with many of the characters, but it never felt like it really succeeded fully at that stuff. From what I've played so far, Three Houses really goes all out on this regard. It's not that the characters aren't still based on archetypes (e.g. Bernadetta is a typical NEET, you have your "ara ara" women, your tomboys, your smug and condescending nobles etc). But you spend a lot more time with each character, see them in a far wide variety of situations. Rather than knowing everything about them from about 3 brief support conversations, you see them change as people over a long period of time, usually on at least a weekly basis. The story itself grows more organically and isn't just "battle 1, set scene for battle 2, battle 2, set scene for battle 3, battle 3" and so on.
In terms of gameplay, I didn't like how Fates and Awakening had this kind of "swarm" gameplay, where it seems that IS were mindful that slow units are typically wastes of space (see FE4 for a particularly egregious example) so they made many units really fast. This resulted in it being harder to have battle lines and proper formations, you just paired up and weathered the storm of a swarm of enemies that could move around your formation and attack rear units in one turn. Three Houses - so far at least - has slowed it down. You actually get defensive blocks of units that you can position and face off against the enemy like a real battle rather than this mad skirmish where everyone is moving 8 tiles. You have gambits that can knock enemies back a tile, like the shove thing in 9. It leads to a feeling of actually being the general of an army rather than a man in the middle of a drunken fight after a football game.
The school stuff changes combat in the sense that you don't end up doing things you wouldn't do in a battle just to grind weapone exp or support ranks. You don't have to be torn between doing the strategically sound thing, and getting this guy to C-rank axes, or getting these to guys to B-rank support. You can still augment their progress but you don't get this odd meta game emerging. It shifts the focus to make the game feel more strategical rather than a kind of pseudo-battle where you're really babysitting units and trying to teach that guy over there to use a lance properly. Sorry for the wall of text, but even this is me holding back. There's a lot to be said about this game. 🙂