You love them or hate them it seems. The guy next to you at the range will love or hate it as well.
I have several rifles with brakes and I enjoy them. That said, I shoot the more powerful (louder) ones at the range less often than I would without a brake. People tend to complain, and I can't blame them.
I have a .270 WBY with a brake and it will knock things off of neighboring benches.
The advantage is much less recoil of course. I wouldn't say the rifle gets more accurate, but maybe in some cases the shooter does. Knowing it won't kick the crap out of you can relax you.
That said, there will be a learning curve. Although the rifle is no longer hammering you, there is muzzle blast in your face. With a .308, depending on the brake, you might feel your hair move and your facial skin being pushed slightly. Some people can't stand the concussion and even complain that it causes headaches.
For me, once I learned to shoot through the blast, I find that I enjoy it. Kind of like riding a bike vs. driving a car.
"If someone has a gun and is trying to kill you, it would be reasonable to shoot back with your own gun." The Dalai Llama (5/15/01, The Seattle Times)
"That rifle on the wall of the labourer's cottage or working class flat is the symbol of democracy. It is our job to see that it stays there." George Orwell