Well, D3 really rocked the boat with how you handle learning new skills, passing around skills between characters, equipping new Mabilities, and increasing character stats. Disgaea 4 makes this a little simpler, with a system similar to the classroom thing but a little more freestyle. They also make the Magichange system a lot more useful and powerful, having it last longer and adding the Monster Fusion system, making monster classes just as useful as humanoid ones for maybe the first time ever. There are (I think?) slightly fewer classes in D4 compared to D3, but they're more unique and interesting. Fewer male/female versions of the same class and more variety and effectiveness.
The story stuff between D3 and D4 is totally subjective, but I preferred D4's. It closes each of its character arcs in consecutive chapters, using a narrative device that's delightfully wacky (and very fitting for Disgaea, but I won't spoil it). I really like the D4 cast - maybe even more than that of D1. I mean, Lord Val is my avatar. Sure, the plot gets weird and melodramatic towards the end, and one or two of the character turns didn't really feel earned, but I was on board with almost the entire cast from the beginning. And I think that the main characters are one of the most important pieces to what makes a quality RPG - Disgaea 4 has a really entertaining cast.
So yeah, refined mechanics that feel less time-intensive than D3's (but not as hilariously exploitative as DD2's), a few fun new mechanics to play around with, and a really entertaining selection of classes and characters. Oh, and for the first time you can edit your base's layout in major ways, including turning ANY MAP IN THE GAME into your base. So many customization options. It's a blast.