I'm only about an hour and half in, but I'm enjoying it. Everything definitely feels very familiar, but it feels like a faster start than BL2 - the first skill point comes at level 2 (maybe 3?) instead of level 5, and the new mechanics (low gravity, oxygen) are introduced fairly early on. As mentioned above, the jump pads and "verticality" are a pretty cool addition. I also like how they're doing the story-telling (minor spoilers, I guess?): Instead of Marcus telling a story about the vault hunters, the story is told by one of the characters as they're being interrogated by Lilith and the gang. Similar to the Tiny Tina DLC from BL2, Brick and Mordecai chime in from time to time with their reaction to the story that's being told, e.g., "Jack did that? Maybe he wasn't as much of an asshole as I thought."
And so far (again, only 90 minutes in) I haven't noticed a ton of BL2 style humor. Then again, the BL2 stuff never really bothered me. I probably put 200+ hours into that game, and I loved every second of it.