Off the top of my head:
- Three characters, Kurt, Riela, and Imca now have unique special abilities that can be triggered at a cost on the battlefield. This uses up points that are separate from the main command ones, but since they're all powerful in their own ways, you're limited in terms of how often the can be used.
- Story progression is back to a linear format a la VC1 instead of the calendar system that 2 employed.
- Emblems or whatever you needed for unit promotions and class conversions are gone. Instead, you can change classes for all characters at any time and instead level them up just by playing through the game normally.
- If you do change classes for the units and have them stay there long enough, I believe they'll unlock potentials that you can then apply while having them fight as other classes, essentially carrying over the perks of other class types to an extent and letting you override certain weaknesses.
- Branching mission objectives and story sequences. Most of this is superficial until the very end, where you do have your choice of two endings, even if one of them is very clearly canonical over the other. It does mean that you can choose what sort of mission you want to engage in at different parts of the story to achieve the objective at hand. Beating the game also lets you play through any alternate paths you missed out on the first time.
- The game does not take place in anime high school.
None of the changes have super dramatic effects on how the game plays out, but I would argue that it does arguably make 3 the most mechanically refined entry in the series, hardware limitations affecting battlefield sizes and whatnot notwithstanding. It's been a while since I've played the Japanese version outside of some light postgame stuff here and there, so I might be missing on more minor details, but those are the big ones from what I remember.