CoD easily wins.
COD VS HALO

CoD does have a story. MW series is focused around Captain Price, Soap, and Makarov, Makarov being the main antagonist.
Ok for multiplayer I would go with Call of Duty
But for story Halo could just be the best science fiction story ever Oh I can still remember finding 243 Guilty Spark on installation 04. the call of duty story was over the top. (exception Ghosts)
Black Ops 2 the first mission has you mowing down hundreds of enimys with an assult rifle... really
but the Multiplayer really has no equel (exept Battlefield but thats a debate for another day)
If I had to pick a game for the singleplayer appeal I would pick halo
but for multiplay it would be BF4 but since that isnt an option I would go with cod

That's cuz BO2 was bad and so was BO1. The MW series was much better. I seriously miss the good old days of Price, Soap, Ghost, Roach, those guys. The old 141.

The thing is, as you play through MW, you actually start to care about the characters. Of course, that effect is enhanced by the fact you're playing from the first-person point of view, but a lot of stuff in games is black and white. In CoD, you get some inside information on what kind of people the soldiers are. imo, you don't really get that in Halo. However, after you've played or watched the entire MW series, you really care for these people and it hurts to see them go.
DEBATE AWAY!