After having enjoyed the first Danganronpa game, I was pretty excited for this one and was expecting it to be more. And in most departments, it delivered. Overall I like the characters more, the more open setting is really nice, and I love the new trial things like the Logic Dive and the rebuttal thing (don't remember the name off the top of my head). There were also improvements over existing mechanics from DR1, for example the closing arguments.
Where this game bombs for me is the logic. I had to continually consult a walkthrough in the game (probably at least five times) to be able to advance in a trial because the answer was either stupid, crazy, borderline nonsensical, or all of the above. There was one specific Spot Selection that was utter BS because it's cryptic as hell and the walkthroughs I found were not helpful at all. I had to consult a youtube walkthrough to figure it out. (If you're curious, it's when you select the Octagon in Chapter 4. Like seriously, how tf do they expect you to figure that out)
And another thing: the story. When you hit exposition city (aka the last chapter of the game), things just get so effing complicated. It's like one giant ♥♥♥♥ where there were trying to fit together the story from DR1 and the new stuff, and honestly I think it's just a mess. Of course, I did like the cameos from DR1 near the end, and the ending sequences themselves were pretty cool, but it was kinda ruined by the crazy plot and dumb logic.
tl;dr DR2 made a lot of improvements to the mechanics and I like the characters more overall in DR2, but the twisted logic and crazy plot kinda bombs it for me. If I had to pick, I would probably say I like DR1 better.