The BATF holds the view that any device that functions as a flash suppressor is a flash suppressor, regardless of its design and intended use. It doesn't matter if it's a compensator, muzzle brake, or flash suppressor by name, but it does matter if it behaves as a flash suppressor.
Open front or closed front (except for a hole for the bullet to pass through) doesn't matter to the ATF. You simply choose the brake that performs in a way that you like. Personally,
I'm not a fan of most brakes due to the significant increase in noise they create, particularly to the sides where your neighboring shooters are trying to shoot.
Incidentally, the BATF's position on silencers is essentially the same. If it behaves as a silencer, it's a silencer, even if it's a potato stuck on the muzzle, though in that case the evidence with either rot or sprout roots before the trial date comes.
CJ