Oh cool, it did become one of the battles. *goes to copy and paste my old answer*
I'd have to go with EA.
Simply put, EA has more games than Activision that I fully enjoy. Also, anything that Activision has that I enjoy, EA has something similar that I enjoy about as equally, though usually ending up surpassing the Activision game.
Activision for me that I can remember has Guitar Hero, Call of Duty, and Tony Hawk games when I used to play those skateboarding games when I was younger.
Aside from Tony Hawk (though I may not be remembering the EA skateboarding game), Call of Duty gets beat by Battlefield for me since I like the Bad Company games better, and Rockband is about as equal to Guitar Hero for me.
Past that, EA also has other games that I enjoy pretty well. Dragon Age for sure. That game was loads of fun. The Lord of the Rings games they've released have also been great, especially The Third Age. Though sometimes lacking, being a Harry Potter fan, I try to give the games at least a chance and play them a little before saying they suck. The earlier ones weren't as bad, and the newest ones aren't the worst games ever, but something almost feels lacking in them. Still good games, though. They, for me, surpass any games that Activision has put out in similar interests (sort of) like Spiderman and such. And whenever, I feel like racing, I can always rely on Burnout to be good, or if I want a change, Need for Speed games are also pretty good in my opinion.
Overall, EA has just appealed to me more so that's why my vote goes to EA.