It appears I'll be first in giving a serious answer.
Black Ops is by far better. MW2 had several basic flaws, and many carried over to MW3. The big ones are spawning (not AS bad in Black Ops, but not good there, either), perks, and Deathstreaks. Black Ops also had itself a better look and feel of sorts. Guns sounded more like guns when you fired them, plain and simple. I'll give MW3 credit for the better campaign, but that was more set up by MW and MW2.
We all know, though, that shooters get their credit from the multiplayer, and Black Ops is much, MUCH better. I remember often thinking MW2 was a terrible game in hindsight (even though I played it to death), but for all of its failings, it was better than Black Ops in terms of the maps. MW3 ruined that. The maps were just bad, no other word to describe them.
I can sit here and whine like a little girl/fanboy about why I hate the MW series in hindsight, but the truth is I played and enjoyed MW and MW2 for a LONG time. MW3 was fail from the start, though, and I'll leave it at that. Oh, and a ranking of the titles offered on Xbox 360:
1. Black Ops--I just said why.
2. Modern Warfare--Its online was better than CoD 2's.
3. CoD 2--I had a lot of fun playing this locally with friends.
4. Modern Warfare 2--I played it a lot, but in hindsight, it was bad.
5. World at War--The game was terrible, actually. However, it added the entertaining Zombies mode.
6. CoD 3--That was a bad game, haha, no question. I barely played any of it, so I cannot really dump on it.
7. MW3--It probably only ranks lower than CoD3 because I played it more, but nothing in this game was done right.