Definitely. Besides the greater diversity of missions and the actual interesting character interactions, the new mechanics are what made me groan when I tried to play a little Borderlands 1 with an achievement-hunter friend.
Each character still has three upgrade trees, but there seem to be about twice as many skills to choose from. Each tree has an ability which dramatically modifies the character's special ability (special abilities also seem to cooldown faster and be a much more important part of the game, both in single player and coop).
For example, Maya. Her ability holds a single enemy still for a few seconds, disabling it and making it an easy target.
First tree, motion: Nearby enemies are launched toward the effect, giving it an area stun and a perfect target for grenades.
Second tree, harmony: You can use your ability to instantly revive a friend, from a distance, instead of locking an enemy.
Third tree, destruction: The enemy is wracked by a series of elemental explosions, including slag (being slagged doubles all damage taken for a while)
If you take level motion AND destruction, all the nearby enemies will pulled into the elemental explosions. Perfect for 1-2 players.
But if you're playing with a good team, it's better to take Motion and/or Harmony. Group up the enemies and watch the soldier nuke them, or the assassin chain-kill them. Being able to instantly revive people is as good as it sounds, too.
I mostly played Siren and Assassin. As assassin I would wait for the enemies to get bloodied, then go into stealth mode. As long as I killed with every blow, stealth mode wouldn't run out, so it was all about finding the perfect time to strike from the shadows.
I guess my point is that the classes play waaaay more uniquely than in the first game. There are still good upgrade paths for single player (Fire-happy siren, sniper assassin, gunzerker... gunzerker) but a lot of the abilities seem designed around natural coop. It's not hard to figure out, either: when the siren locks an enemy, it's held aloft in this giant purple aura and shouts curses at the players. It's pretty obvious where everyone should focus their fire
I played through Borderlands 1 twice but the coop didn't really click that well. This one's a lot better.
Edit: I really wasn't expecting a good story, but it happened. Despite the cartoonish graphical style, the characters get a surprising amount of depth. There was a part where I refused to do side missions even though I kinda needed the levels, because I was too angry at certain events. That was difficult, but fun.