I honestly think that BL2 is more of the same as BL1. Sure there are new characters and a couple new gimmicks, but overall it's very similar in my eyes. I'm only lvl 14 so maybe it gets better later, i dunno.
One thing that i dislike, is that very few guns are usable. In fact, it can cripple your early game a bit if you're unlucky (I noticed that when I restarted from lvl 7 to lvl 1 because i did something stupid and wanted a fresh start). Some other guns, on the other hand, feel overpowered in comparison.
Not long ago, I was still using the first sniper rifle you get when you fetch yeti hair for the 2nd NPC you meet. It had a 180% crit dmg bonus and 90-something damage, so i could one-shot almost everything (doing ~500 dmg, to be compared with the ~20 per shot for starter guns). In fact, the sniper rifle i'm using now is the same but higher lvl. The only other gun i'm using is the pistol with the infinity symbol, basically it's like a machinegun with infinite ammo. Those two are good enough that i'm never using the gun in the third slot, since i can't find anything as good as those. Most shotguns can fire only once before reloading, and in fact most guns have such a small ammo clip that you feel like you're spending more time reloading than shooting. But you can also get lucky. I once got a sniper rifle with a bigger ammo clip than most other guns i had found (19 bullets), and it fired fast enough that i could use it as an assault gun.
It's also true that you can't carry much ammo. In fact, i often (at least 3 times now) had to run back to the ammo store to finish a mission objective when it asked me to use a specific gun. I know that you can upgrade storage with eridium, so at least it won't be a problem forever.
Oh and one last thing : there are way too many containers to open. Most of them only have ammo and pocket change, and there are enough types of ammo that you keep finding stuff you don't use anyway. If there was less chests but more in each of them, it would feel much less like a chore, i think.