I'll just type any thoughts that plop into my head
Battlefield Bad Company feels like it has more weight to it when moving around. I read some people saying they thought it felt sluggish... but I took it as it feels more like you're lugging around all your equipment.
Tanks/Jeeps/Choppers are very cool - although I can't control the chopper online even though the SP mission in the chopper was easy.
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Different classes seem to have more specific uses and overall lends towards a better TEAM based online game with BF - You can't pick the rocket guy and blast everything with a silenced machine gun and then sniper someone and then heal yourself. Each side needs a good balance to win.
It's like a big game of Rock/Paper/Scissors where you need Demolition guys laying anti tank mines and blowing shit up with their rockets and also getting into CQ battles with their shotgun.
A few snipers (Recon) out to snipe out attackers, use their air to ground missile to take out vehicles and to spot enemies for the other teammates.
Assault are the grunts - you need a few of these guys to soak up the bullets for you if your another class - and they have the 'life2' upgrade that injects them with a health boost when they're hurt so they can keep going and going for longer than the energiser bunny.
Specialist class is becoming my favourite now for attacking - you have the silenced weapons so you don't make a load of noise when killing people after flanking them. and the C4 is one of the best weapons in the game and is massively underused. You run up to a gold crate, throw all of your C4 down... step away... detonate and either instantly destroy the create or damage it really good.... the best bit is you don't give away that your next to the crate like if you planted the bomb there. AND... you have the tracer gun which enables anyone playing demolition to lock missiles onto your tagged targets and fire homing missiles
Support class was my favourite attacking class though. You have the medic packs to heal yourself and team-mates. the mortar strike to call in a strike where ever you aim and a huge feking gun
As seen here after taking a chopper down
http://i147.photobucket.com/albums/r320/KRad_bucket/ChopperDown.jpg
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I've not noticed a big difference in classes with COD4 other than if you pick the sniper class. The rest all feel the same and as you can kill with a few shots it doesn't really matter which class you pick as long as you can aim straight.
COD4 has a better ranking system and challenge list. Not that BF's is bad... it takes a long time to rank up to level 25 and the trophies/awards are going to take a while to get. But CODs just seems bigger and seems to have more to it.
I could be wrong but that's just what it seems to me.
Random little extra thoughts
BF has bigger and probably better maps.
COD4 has more game types
BF Has the destructible environment
COD4 has the better SP campaign
BF has online track able stats and photo mode to show off
COD4 is easy to pick up and play well at
Which do I prefer...
I'd probably pick BF BC