Call of Duty is mostly infantry, one-on-one deals in small/medium maps and relatively small teams of players on each faction. Depending on the mode, there could be some objectives, but the most popular mode, by far, is deathmatch and team deathmatch.
Battlefield has infantry too, but the distinctive difference is the inclusion of several vehicles, which are a must because the maps and teams in BF tend to be a lot bigger. The most popular mode is domination, which is a control points mode. Also, people in BF are organized in squads, which are smaller teams of players within overall factions and teamwork is heavily encouraged. DICE included level destruction in the game, which is a nice feature but not necessarily game changing. Because of this and the abundance of several kind of vehicles, Battlefied multiplayer is more prone to emergent gameplay.
Personally, I find BF more fun. Because of the larger maps, it could be rather lonely at times, but the randomness of the games adds a lot to the experience.