The answer is YES! YES YES YES!
I found Pokemon Black and White to be the first games in the Pokemon series that deeply disappointed me. I found the music to be, for the most part, boring and uninspired. They took away so many things that had come to make playing the Pokemon games so interesting and varied, such as the berry-growing and the Pokemon contests (which were replaced by musicals). And I disliked the direction they took with the story. I would have preferred if they actually just kept it as before, rather than introducing the idea that maybe having Pokemon battle each other wasn't ethical and then completely going with the argument that "It helps Pokemon reach their true potential." As a 20-year old college student, it just seems a bit ridiculous, though I wonder if children blindly accept this explanation. Also, I felt that the games were lacking post-game content that was varied. The Battle Subway is a challenge, but after a while it gets boring as there is not much variety to it.
Pokemon Black 2 and White 2, however, deliver where the first two games did not. First of all, the music in these two games is beautiful. There are many great new themes, especially in the new beginning cities and towns. The theme for Aspertia City (that's right, CITY - it has its own gym and Pokemon Center) is a breath of fresh air, and completely different from all starting themes before it. Quite honestly, it is one of the best in the series.
Story wise, I feel that they toned it down with all of the ethical stuff and turned it more into a traditional hero-versus-Team Rocket story, which Game Freak has always done well.
In terms of post-game content, this game has a lot to offer.
First, there is the Pokemon World Tournament, where you can challenge past Gym Leaders and members of the Elite Four. You can also participate in competitions where you only battle in a certain style, such as double, rotation, and triple battles. I thought this was excellent since these modes are barely used in the storyline.
There is also the White Treehollow and Black Tower, where you have to go to the lowest levels of these locations. The trick is, you don't get to bring items with you and the place is infested with Pokemon trainers with strong Pokemon. I have actually lost various times here. It is challenging, and I like it!
In addition, there is also Join Avenue, a place where you can buy loads of new items, increase your Pokemon's friendliness, and even buy your Pokemon food that can raise their levels and their EV stats, which makes it easier to train Pokemon for competitive play.
Also, there is now a medal system - basically, its a trophy system. It is pretty addictive. The game also gets a challenge mode! If you get the key yourself or have someone give you the challenge mode key, you can increase enemy levels and AI! Which is a big plus for me!
A few other changes that I liked about Pokemon Black 2 and White 2:
+When you run out of repels, a little text box pops up and asks you if you'd like to use another. It is faster than having to open your bag and pick it again.
+You are no longer limited to Unova Region Pokemon.
+It is easier to move Pokemon around in the PC. You can actually now choose whole groups of Pokemon to transfer at once.
+Every gym has its own theme! This is excellent! I hope they keep doing this for all new Pokemon games, because it really helps give each gym its own feel.
There are a ton of kool, new additions to the series this time around. So if you are wondering if you should get the sequels to Black and White, I say do it NOW!