The remington 700 police edition with heavy barrel profile is what I have in 300 RUM (they make the same rifle in .308 and is considered the most accurate .308 rifle in the market today)...
I like browning more than remington, but when it comes to those remington 700 police rifles, NOTHING beats them (just my opinion)....
Just remember, this is coming from a guy that actually owns one (but not in the specific caliber you want)...
Now if your talkin about a-bolt browning vs remington 700 (not the police edition) then of course, a-bolt would win with ease.....