Borderlands 2 improves upon 1 in every way, from story, to weapons, to dialogue, the game is great, bring friends.
Borderlands 2 improves everything the first did well, and fixes everything it did wrong. The story is actually something to care about this time around. Handsome Jack is one of the best villains in a shooter these days, and constantly interrupts you with humorous dialogue.
The environments are more diverse, ranging from snow, to grassland, to desert, to mountain, and more. The classes play much better, each offering their own unique abilities. The weapons are unique ranging from a flame sniper to a disposable plastic pistol which explodes when thrown. The game clocks in at about 20 hours, but there are a ton of side quests you will get caught up in, most of which you won't experience until your second playthrough.
Make sure you bring friends, because the game does not feel as good single player only (although you can jump into a lobby through matchmaking). The game does have a few difficulty spikes though, and the final boss is a grind fest.
Overall, Borderlands 2 is a fantastic game which improves upon its predecessor in almost every way. Just make sure you bring friends.