Idaho CTD, I judged the issue on the side discharge brakes being louder by how my ears rang more than the Radial brakes.
Sound is transmitted to the inner ear:
a. auditory canal
b. ear lobes
c. concussion on the skull transmits vibration to the inner ear
So, concussion is a major issue and covering your Ear lobes is also critical in reducing hearing damage.
For shooting off the ground, Side discharge brakes is your only option, and I use good electronic ear muffs.
lancetkeyton, you are in serious trouble. You have hearing damage to begin with. Now, you shoot unprotected. What you do not realize is that more hearing damage accumulates over time, it is accumulative...keeps getting worse.
If you can find a comfortable set of electronic ear muffs to use while you are hunting, you will never go to the woods without them again, as they give you a serious hearing advantage, discovering a whole new world that you never knew was out there.
Deer do a lot more short wheezing, grunting, bleating than you were ever aware of previously. Hogs do a lot more grunting than you were aware of, you can hear them grunting at a distance.
Some side discharge brakes are a LOT worse than others. Short barrels or 20" are a lot worse than a 26-28" barrel in concussion. Some calibers and in particular some powders have more muzzle pressure than others.
You get one set of ears, protect them best you can.