Most pros have ridiculously low sensitivity for better accuracy. I just can't do anything on low sensitivity, sadly. I have it on 11.
I think it's basically a given that lower sensitivities are better in competitive gaming. I remember when I played Counter Strike 1.6 having sensitivity more than 2.5 (PC gaming) was already considered too high.
CS is a very different game to CoD though, CS isn't as fast (imo, been playing it since about 1.3) and you don't have people spawning close-by on either side of you like you do in CoD, it also doesn't have crazy in-built aim assist and the headshot multipliers in Black Ops II are pretty poor for most weapons (some don't even have any).
High sensitivities have the advantage of quicker turn speeds and being able to get generally on target quicker, the downside of course is that micro movements aren't as precise but that's dependant upon skill (and due to the ttk and poor headshot multipliers for most weapons being generally on target on someone's torso is really all you need, precise movements for headshots aren't worthwhile a lot of the time). If you get used to higher sensitivities you can make the movements to be on target faster and you have the benefits of the quicker turn speed.
Depends on the weapon and playstyle really though, but generally I'd say CoD is well-suited to high sensitivities whereas CS isn't.
Currently playing: Metal Gear Rising demo, Lag Comps II Up next: Max Anarchy, Hitman: Absolution