IMO no muzzle device lessens the amount of noise heard below what a target crown creates except a can. Apx 2 weeks ago we tested 8 different muzzle devices and a target crown for noise using a meter. The target crown, A2 flash, Vortex and our flash all produced 81 db.
Big ports mean big noise, all of the brakes/comps with large side ports or many small ones are IMO too loud to use without some sort of hearing protection even for 1 shot while hunting.
Everything is a trade off, to get great recoil reduction and muzzle control the ports must be large enough to redirect the gases to the side instead of out the front of the muzzle, large ports make noise so no, nothing that reduces muzzle rise will also lower the noise level.
Some brakes are much more efficient than others and reduce muzzle rise, some in different ways. Brakes with big side ports try to reduce recoil to the point the muzzle will not come up, other brakes with top ports can keep the muzzle down much better with smaller ports because the gases are being directed up which push the muzzle down. The SJC Titan, TTI eliminator and all of our brakes have those top ports.
There are some new comps that are half brake and half flash reducers, they can reduce muzzle rise while not increasing noise to the point they can't be used without hearing protection.