IMHO, no need for a brake on a .308 unless you are doing some kind of varmint hunting and want to watch the blood and guts in the nightforce. Recoil on a .308 is very manageable, especially from a 700 with a heavy barrel and normal loads.
With a brake you exclude yourself from competitions such as F-class, where no breaks are allowed, if you go hunting you need to be wearing your ears at all times otherwise you, or your partner, go deaf., and It is also irritating to your neighbors next to you at the range.