Or does it matter?
I have a Resonator K in lockup. It comes with one QD Muzzle Break. I have multiple rifles so I bought a couple more.
Well one arrived and it is the Flash Suppressor not the Muzzle brake.

Is there a difference between the two in sound suppression when used with the can?

If bother are QD and inside the can when attached, I don’t see how either would make a difference. I’d prefer the FH; less headache when firing unsuppressed.

All things equal, the brake is more effective. It does a better job at disrupting the flow of gasses forward by allowing expansion sideways where a flash hider is still mostly directed forward.

It's not substantial and you should still choose your muzzle device based on how the rifle will be used. But if it's staying suppressed 100%, a brake as a partial or sacrificial blast baffle will increase performance over a flash hider.

Definitely agree that a brake taking some of the beating is a huge perk. I am hard pressed to shoot a gun without a can at all, but I sure as hell wouldn't with a brake, so it'd be as Rustpot said, in a 100% suppressed setup.

When shooting suppressed, the difference in sound levels using a brake over a FH is negligible. The main value of a brake is acting as a sacrificial baffle to increase the longevity of the suppressor. The flip side of a brake is when shooting unsuppressed, it makes the gun louder, more blast, and does nothing for flash. The individual decision is usually based on whether you intend to shoot the gun unsuppressed or not.

I have not studied this issue in any way because when I don't have a can on a gun I want a FH and not a brake. But when I was researching my Thunderbeast purchase I stumbled upon a good discussion on this issue in the product literature for their DOMINUS-K-SR suppressor.
My conclusion is that this sacrificial baffle benefit is completely irrelevant for any normal person and/or firing schedule.
In terms of suppression I have seen some tests that show measurable differences on surefire cans between the FH mounts and the brake mounts as the brakes alter the gas flow. I have never really cared about this issue as I'm using the FH mount in all cases and it doesn't suffer from the problem. Some research for your specific can/mount system may provide different guidance.

I think you see more of the sacrificial benefit on a short barrel. I had a AAC 51T brake on a 10" 5.56 in the past, and the brake took quite a beating. I'd assume that beating would be inflicted on the can a bit more, if the brake wasn't there.

Sounds good.
The brakes will go on the guns that will likely not be shot unsuppressed and the FH on the gun that will see some unsuppressed.