I do think this is a better game than the first one, but not by much. I'm one of those people who didn't even really hate XIII at all, I just thought it was pretty meh until you got to Gran Pulse - where things opened up and became more fun.
This game has better characters and was more enjoyable to play through overall (with some caveats I'll explain in a bit), but the story is very silly, and a lot of it feels like filler. I will say the ending is really strong, and it definitely made me actually want to play the 3rd game - something which I was doubting I was going to do while playing through most of this game.
The game's side quest design and the fragment collection are probably the worst part of the game, to be honest, and it takes up the most time. Some of it is just really annoying and I didn't enjoy it at all, especially when you had to visit multiple time periods - and loading screens - in order to complete convoluted fetch quests. I didn't even get all of the fragments, because there's a bunch of shit you need to do post-game that I was just not feeling or interested in, such as completing the entire bestiary and winning a certain amount of coins in the casino. It definitely took me way longer than it should have to complete the game just due to my gaming OCD making me collect useless fragments that I should have honestly just ignored.
Overall though, gripes aside, I did enjoy my time with the game, and as silly as the story was, I enjoyed going through it for the most part. Onwards to the 3rd game, I suppose.