Starting with the former, let me tell you this. The people you play Battlefield with (your squadmates and or friends) will make or break your experience. Unlike Call of Duty, there is no way around it, you really need a squad in BF, to the point that the game will even put you in one, and if you don't play well with others, or the others are particularly dumb players, expect a frustrating time.
The inverse is the experience I had in Modern Warfare. I often found I had more fun playing the single player or special ops mode of Modern Warfare and playing that either solo or with just 1 friend (there really should be another option for spec ops, but yeah they limit you to 2 player co-op). I'm not going to say it's not possibly related to my general inability to have fun in multiplayer of Cod though, but the inclusion of bots made the game and it's predecessor much more fun.
Both games have a co-op, no deathmatch inspired mode, but here Modern Warfare really pulls ahead, because it allows you to play that content alone, not forcing you to either play with friends or randoms like in BF. Well that's mostly true. There are a few missions that require 2 players in Cod's spec ops, but there are enough that don't to make up for it. Unlike Battlefield, which seems to be trying to tell you a parallel narrative of the main story through the co-op missions. The problem is, all the BF missions aren't fun, only a few of them, and you have to play through all of the them multiple times to unlock the guns for multiplayer. It's not mandatory to complete, but if you're a completionist, or you want some different guns, then you'll take a stab at it.
Ultimately, you can only compare the two games on the things they try to do. It's easy to say BF3 is the better game, but then if Cod had BF3 sales Cod might be canceled. They're for 2 different audiences and there is some blend, but in my opinion, BF3 needs to stop trying to be COD in so many ways and give more content.
There's a tirade I usually go on, about the lack of consistent BF content updates (maps, weapons, etc), and I don't think Dice or EA are about to change anything about it.
Now I brought all this up for 2 reasons.
1) To get it out of my system
2) To mention Planetside 2 coming out later this year.
Now Planetside is one of the best ideas for a FPS I've ever played. It goes past just deathmatch and basic objective to through you into a persistent world of guns and objectives. Planetside, also happens to be about a decade old, and it's successor Planetside 2 is shaping up to evolve the game in interesting ways.
In case you were wondering, of course I have a video about it. This one is a bit older, but it definitely explains what to expect from the upcoming free to play shooter.
Yep, Free to Play. You can register now for the beta at Planetside2.com.