Not including Advanced Warfare as it can't be considered Cod.
The mechanics of battlefield are simply superior. Accounting for bullet drop, leading targets, vast array of vehicles and destroyable environment.
But COD isn't trying to be realistic. It's trying to be fast paced and generally fun. If it weren't for modding that'd definitely be considered achieved I think. I also find the class setup system a lot better in general with COD. And though I'm sure many would argue against it, but I feel especially with Black ops 2, MW3, and even MW2 that the weapons are generally more balanced. Of course you'll get anomalies like the FAMAS or AUG, or ACR but for the most part I feel you can get kills with the worst weapons fairly easily if you're conscious of perk/attachment setup. I personally don't feel the same comfort-ability with Battlefield.
Either way, I think Battlefield is a better game overall in the impressive intricacy of their games, but I enjoy COD more for it's fast paced straight back into the action feel.