Let's just state this, White and Black 2 are two incredibly different games, unlike most prequel-sequel connections.
The Pokemon that appear in White are all Gen V. (This enraged me when I first got the game. Lol. xD) The only non-Gen-V-Pokemon are found post-game. :( So, if you prefer older Pokemon you should DEEPLY consider Black 2, where are variety of Pokemon appear, compared to the game's prequel.
As for the storyline, I'm gonna try my best to sum this up. To my knowledge, I can't say there is any continuity between the two games, except for the fact that the games NPC's keep on saying
>I once saw this trainer two years ago, who did this and that and it just... touched me. I hope they beat the game and their future selves will play the sequel and will talk to me again. Hey, I think I know you somewhere! Are you that trainer who just [blah blah blah] cows.
And all that stupid reference. Apart from that, there is no continuity to my knowledge.
A storyline is extremely opinionated, so I can't judge it that well, but both have good storylines. If you like a bit of destruction here and villains-who-turned-into-heroes thing, than choose Black 2. As for White, there is no continuity (obviously) but if you like a bit of friend-turned-to-enemy here and two-rival-nonsense there, choose White. Also, in Black 2, the order you approach the locations are completely reverse (so, Route 1 in White are Level 2, Route 1 in Black 2 are Level 50-something)
It should be noted that you do have two rivals in White. (Or, at least two people that battle you frequently throughout the game, but rivals for short. xD) There are also more locations in Black 2, so if you like a longer storyline that go for it.
If you like completing your Regional Pokedex, there are disadvantages for both games. They are both minor. In White, there is one Pokemon (and it's one Pokemon it's evolutionary line) are unavailable under all circumstances (I think it's the Braviary, or it's version-opposing exclusive) since it does not appear at all in the game, unless you trade from another game. (i.e. GTS won't work) Also, in Black 2, you cannot breed until post-game like in FireRed and LeafGreen.
So... you're choice, I guess. If you want me to clear something up, ask me and I'll talk about it.
Hope I helped. :)