First things first, I own Borderlands 1, and all downloadables. I've beat the game several times, and camped Crawmerax for more hours than I care to admit. That being said, I think this game takes what was good about the first, and improves on it.
Starting with your character progression, the skill trees have been expanded for different types of play. For instance, the Assassin has 3 different skill trees. One for Melee, one for long range, and one for other character benefits. It provides many more options, plus, if you don't like what you've done in the skill tree, then you can (for a fee) just change your point allocation.
Now, I mentioned a long range Assassin, which is my typical type of play. It was one thing that frustrated me in Borderlands 1, because enemies would be at a long range, and still shooting me. Or they would come running and be way too close, way too quickly. But now, sniping has turned into a viable play type. I can stand hundreds of yards away and make my shots. As long as I have a quick recharge shield, those occasional shots that make it to me aren't an issue.
Speaking of shields, that's another change, that shields can vary not only the rate of recharge, but how long you have to not be hit before it starts to recharge. In a long range situation, I like a short time before recharge, at a penalty of overall shield strength. If you prefer, though, you can get a stronger shield at a cost of health. Or a shield with spike damage (Injures enemies if they hit you) Again, it just provides even more options for playstyles.
Remember those achievements that were in B1, that would then give you exp. when you completed them? How many hours did you spend idly running over critters to get the next achievement and 5000 exp? Well, those are back, with a twist! Now, each achievement earns you "Badass points". What are those, you say? Simply put, they allow you to improve character aspects across ALL CHARACTERS on you account! You want more accuracy in your guns, spend your badass points on that. You want a faster shield recharge, or more elemental damage, spend it on that. Either way, it works great. This also takes the place of mastering the various gun types, which doesn't exist anymore.
I mentioned running over critters, and that's also changed. Oh, you can still run them over, but the amount of damage is less, and I've spent several minutes on various animals backing up, driving forward, backing up, driving forward. You want to move quickly, you're going to shoot your way out now.
Lastly, B2 has now brought in this new element called Eridium, which functions like a currency in game, for special items. Whereas in B1 you could buy magazine capacity upgrades with in game currency, now it requires Eridium. But not to worry, it comes all over, from various enemies, or in lootables. Eridium is also used to increase backpack capacity, as well as bank capacity. That's right, I said bank capacity. You no longer have to buy a downloadable pack to get a bank, it is part of the game. Not only that, there is another bank that allows you to safely transfer items between characters on the same account
All in all, if you liked the first one, you'll like this one too. The graphics are even better, and gameplay is great. I wish the opening sequence wasn't so long for a new character, but other than that, I am having a great time playing!
Now, one caveat...there is a lot of language in this game, so it is probably not the best to be playing with small kids around, but with the amount of blood and exploding heads, you probably shouldn't be doing that anyway.