A silencer is caliber specific, and usually made for a particular case volume. No problem at all switching between rifles that shoot the same cartridge.
As for switching between calibers, you can go down a couple of calibers with either.
A .303 silencer will work perfectly on a .308. I doubt there will be any noticable difference in sound level at all.
The important thing with the silencer is the case volume it was designed for. A .308 silencer might not be suitable for a 300 RUM or 300 H&H, for example. The more powder, the bigger and stronger the silencer has to be.
Muzzle brakes lose very little efficiency when installed on smaller calibers than what they were made for.
