shoot'n hogs --
Velocity first. It depends on how the brake is added. In general, physics would indicate that if you start with a 24" barrel , cut it back and add a brake, you can expect some reduction in velocity. By the same token, if you leave the barrel at 24" and add a brake, you can probably expect a slight gain.
As to ballistics, it again depends. If you add a brake to an existing rifle, chances are excellent that point of impact for given loads will change. Not a big deal, just rezero.
The BOSS system allows the shooter to adjust the length of the barrel, thereby affecting its vibration pattern -- the result is that the shooter can "tune" the rifle to the load rather than tune the load to the rifle. FYI, some BOSS systems are braked, others are not.
Braked rifles may provide the shooter with an edge over unbraked systems by reducing recoil to more manageable levels. This will, of course, be highly dependent on the shooter, rifles and loads in question.
There is one last "effect" of muzzle brakes that I should mention. My club, and others, have special restrictions on rifles with brakes. In the specific case of my club, shooters with .50BMG and ANY braked rifle must notify everyone on the shooting line of his intent to shoot such a rifle. If any person objects, the rifle in question cannot be fired. There are at least two good reasons for this: 1) brakes significantly increase blast and noise levels to the sides, and 2) brakes often cause rifles to spit material to the sides, often hitting bystanders. (whether this "material" is unburnt powder, or bullet shavings is totally irrelevant). Being unable to shoot the rifle has a most detrimental effect on ballistics and velocity!