I wouldn't say drastically improved, more like a lateral shift. The biggest change I remember is that VC2 has smaller maps because of PSP memory constraints, so each mission is split up into several different areas connected by base camps. There are also tank upgrades, more classes and a more robust class upgrade system with varying roles, though parts of that system are straight up garbage (you have to collect a bunch of parts to upgrade each character, and those parts only come via random drops, so you could grind out missions for hours and still not be able to upgrade someone to a Fencer Elite because the RNG didn't give you that last part you needed).
VC3 gets rid of that part system in favour of a more streamlined XP-like system--the more you use a character, the faster they get to upgrade to a better class. You can also switch a character's base class at any time (ex. from Shocktrooper to Scout) and if they've already unlocked more advanced classes in that group I think they have access to them immediately as well (ex. Gunner or Shocktrooper Veteran in the Shocktrooper group). Otherwise it's very similar to VC2.
P.S. Stupid VC2 high school bullshit. Worst part of Valkyria Chronicles ever.