i would have to say both have their pros and cons depending on your game style.
DMR's are for the more sharpshooting and well trained marksmen, and i'm not sure if it has a slight DMG boost but I do know whether its impact is equal or not it is faster to fire more bullets giving more flexibility to fix a mistake in close quarters combat but a slight however it is a gun for medium/ long distance shooting and isn't really reliable in swat. or any close quarters fighing
The battle rifle on the other hand has increased impact but slower clip fire than the DMR meaning you may experience pressing the fire button but it doesn't fire immediately giving the opponent a split second to react. However! it dosn't fire one bullet but a pulse of bullets meaning you can fix your aim in the middle of your shooting. this is very useful in swat if you are the one who is full assault.
the summery of the two is if you are more aggressive in multiplayer and dont have much or dont care about your accuracy the battle rifle is for you, if you are the sniper or more supportive from afar then the DMR is for you