Here's the deal: brakes and suppressors both reduce recoil by transferring some of the momentum of the high-pressure gas that exits the muzzle to the rifle, effectively pulling it forward to counteract its rearward momentum due to bullet+gas impulse.
The most effective rifle muzzle brakes have a series of flat plates (ie a surface "normal" to the bullet path) approx 1" plus or minus a little bit in front of the muzzle. The has impacts these plates and pulls the rifle forward. After impacting these plates the gas is directed to the sides and out.
Suppressors have a series of baffles (a lot more than the brake and more sparsely spaced) that are designed to catch gas and turn sound/pressure into heat. They do this by delaying the gas release. In a bolt-action rifle (ie with a closed breach), the gas that was captured by the baffles is delayed in the suppressor but is ultimately pushed out the front. This is why suppressors produce a recoil impulse that is spread out over time, but is technically a little more than what the best brake would have.
I have extensive experience firing rifles from .223 up to .50 BMG suppressed and with a brake. As sort of a general impression, from .300WM and down, the suppressor feels like it has about the same or less recoil than a brake. Larger cartridges, such as .338LM as a particular example, have more recoil with a suppressor than the most effective brakes, but the recoil is more of a push than a hit, and the reduction in overpressure and transformation of the recoil impulse itself is "worth it."
Suppressors that have a brake "inside" -- that is, screw over or attach over a muzzle brake, perform substantially the same recoil-wise as a suppressor. This mounting system usually involves some compromises in terms of suppressor design in trade for recoil performance when the suppressor is absent. Since there is no place for the gas to go other than hitting the inner suppressor walls (after hitting the brake plates/ports), it is pretty much a suppressor for the purposes of my third paragraph, as opposed to a brake in which gas can actually ultimately exit some direction other than forward.