I can't speak for Battlefield, but Modern Warfare is shit.
CoD4:
3x frag
noobtube
stun noobs
ak-47 / ak74u / m40 being ridiculously op
m40 acog giving automatic 1hitkill
m14 / g3 being ridiculously up
shotgun noobs
p90 noobs
dead silence perk ruining the game
steady aim w/smg turning smgs into sniper rifles with no need to use irons
CoD:MW2:
M/L/C (Marathon/Lightweight/Commando @ TacKnife) which singlehandedly ruined the entire game:
http://www.youtube.com/watch?v=yxtXK6sYBcA
Marathon: Infinite sprint.
Lightweight: Faster basic movement speed.
Commando: Triple knife range (Knife lunge is a 1 hit kill and locks on if the target is in front of you)
Tac knife: Faster knifing.
So you'd get dickheads managing to play quite comfortably by running around at 200mph in full military gear owning people with GUNS with nothing more than a knife.
Killstreak rewards: The expansion of killstreak rewards made them the core of the game, and thus being killed by luck or similar made the game a factor of ten more frustrating.
Bushmaster ACR: Has *no recoil.*
http://www.youtube.com/watch?v=J1xeAKNxCrY So basically MW2 became ZARK Rifle Mode.
I can't speak for Battlefield, but personally I find CoD the most unbalanced shit in history, and the developers don't give a shit about the gameplay problems when millions of people are playing the game. Hell, you still see people in CoD4 who don't even know that putting a red dot sight on an AK reduces the lowend damage from 30 to 20, and these people think they're good.