Good: More colourful than the first game, more enemy variety. Most of what was great about the first game is there.
Bad: Loki is unbearable, combat is visually messy in a way that fairly often makes it hard to tell what's going on (can't recall ever having that issue in the first game), the enemy designs aren't as cool as in the first game, the pacing is inferior, flying battles are lame since from a functional standpoint they do little more than restrict your movement options, Umbran Climax looks cool but you're practically invincible during it which is a bit boring, the selection of weapons is overall slightly worse than in the original (no shotguns, the flamethrowers aren't as cool as Durga, the new whip doesn't look or feel nearly as satisfying as the old one even though it is more useful, no ice skates -- you can skate on the chainsaws but they're not nearly as fast -- etc.), and the game never gets as crazy as the most climactic parts of the first one (boss fights in particular don't feel nearly as spectacular). Also, going from having all of the moves, weapons and accessories in the first Bayonetta to being forced to purchase basic shit like the stinger all over again feels kind of crippling.
It's just not as good as the first one. Still, I enjoyed it a lot, and I'm definitely going to go through it again on Infinite Climax.