Well in terms of BF2 vs. MW2 . Big difference, BF2 is much larger in scope, maps are huge, you fly helicopters, you drive tanks...you destroy entire buildings. MW2 is much more "in your face" personal where BF2 it's more about team work and more "calculating" . In fact i'd even go as far as saying , MW2 emphasize KILLS and BF2 emphasize OBJECTIVES .
Both games at their cores are still pretty much shooters and the differences might be very subtle in terms of actual FPS gameplay, you'll get snipers and campers and players who just don't know what to do and limited amount of maps etc etc. So it depends what exactly was annoying you about MW2...
As for Dragon Age vs BC2 . Again, if you've been playing MW2 extensively and basically are tired of it , then i'm not sure BF2 is going to mysteriously rejuvenate your interest in the online FPS-genre. You might like BF2 more or less, but i think if you're not into the whole serious clan play , it might get old just as quickly as MW2.
Now DA is a good game, although admittedly it's not my favorite, it is still too linear for my tastes. If you liked KOTOR and Mass Effect you'll like this, but it has an end, there is no "multiplayer" part that might make the game last longer. So BF2 certainly have alot more longevity, as in you chances are people will be playing it months and years from now. DA, you'll complete in say 50-100 hours of gametime and most likely not play ever again, if yoo don't get into dragon age it might be over much faster. BF2 you can at least fire up on some random day, play an hour, and quit....so that part is worth thinking about. However again if you already have MW2, i guess you can already do that, so having both MW2 + BC2 might be overkill....unless there's something that you hate about MW2 which might be great in BC2.
Personally i dislike MW2 because i'm a "mediocre" FPS gamer and MW2 place too much emphasis on my personal aiming/shooter/killcount ability where BC2 you can actually do well without killing everyone [i.e. you can support the team with healing/ammo/repairing and can sneak around capping objectives].
