Depending on the setup, muzzle brakes can increase both accuracy and velocity, and they will almost always decrease felt recoil. For example, a .25-06 is pretty comfortable with 3000fps out of a 26" tube - that's about the perfect length barrel for that caliber. If you shorten the tube to say 22" you could lose maybe 200fps. If you have an aftermarket brake installed on a 26" barrel, the bullet still has 100% of the gases behind it that it would without the brake, so there's no loss of velocity. If the barrel has to be shortened for some reason to have the brake installed, then yes you will lose some velocity, but not hardly measureable.
Most brakes are made so that the hole is oversized enough to let the bullet go through without touching the brake, and they all have holes or slots in various places all around the brake to let gasses escape. Since the brake isn't 100% holes, there is still some thrust being exerted on the bullet from the gas, so velocity may increase depending on the length of the barrel. For the '06 we're talking about with a 26" barrel, there's little velocity gain past 26" even in a sealed barrel, but a brake on a 22" barrel on the same gun will probably increase velocity slightly.
As for accuracy...the holes in a brake are normally pointed somewhat back towards the shooter (some also point out and up to keep the muzzle from rising). The velocity of the gas escaping through the holes helps counter the backwards thrust of the rifle, and helps to offset recoil. This also directs the sound out of the holes in the direction they're pointing, so the sound goes back to the shooter more, rather than towards your target. Anyway, the reduced recoil often gives the shooter more confidence that he won't get the tar kicked out of him, so he tends to hold the gun more steady and have a more consistant and gradual trigger pull. Some brakes actually do increase accuracy, but I don't know all the physics of why just yet. When I figure it out I'll let you know