The problem for me is that i cant get into arcade style shooters, i hated halo for example.
I did very hardcore milsim airsoft for about 4 years, and one of the guys who taught me to play spent 14 years in the canadian airbourne (the precursor to jtf2, they were basically canadian SAS)
So playing a shooter to me, one of the important things is realism.
Great example of one thing that drives me nuts in COD is they got the stats on so many weapons wrong. I greatly prefer the way battlefield does it, they give you the caliber and type of rounds that the gun uses, they give the rate of fire, and a rough estimate of range. (Which should be obvious, longer barrel = longer straiter trajectory)
The only thing i liked other than the storyline from mw3 was one of the attachments for the guns. Its the eotech xps holo sight, with the flip to the side monocle basically giving you an acog and a holo sight in one.
Yeah I can see where realism would be a requirement for you. I personally have only sampled the one game, so I can't begin to compare them... although I must say that the "unrealistic" factor in MW can actually make it more fun. Gives you the feel of an action movie, which is obviously much different from real life.
Also, Modern Warfare has a great story, as you mentioned, and a soundtrack by Hans Zimmer. That wins it MAJOR points in my book.