I have a Bushmaster 16 with break and it seems very loud.  I know about ear protection and I always wear it but  with Q1313, it's a lot of noise for a little AR.  Does the choice of barrel length 16 vs 20 along with the choice of muzzle break and/or flash supressor greatly influence how loud your rifle is?  If I was ever in a an actual big time shootout, without ear protection, I'd be deaf.

The brake has more to do with perceived volume than the barrel length on your particular rifle.  I can shoot a 16" without hearing protection and barely get a ring.  With a brake it about peels my eyebrows back.

These are my thoughts on sound and shorter barrels. This is based on multiple readings and personal conclusions. I am not an expert by any means.
The 223 round and 20" barrel are optimized together during development by Stoner. That is, the 223 powder is "fully" burned as it travels the length of the barrel.
As the barrel is shortened, some powder is not fully burned and literally explodes when it hits the air (shorter barrels have greater flashes) and generates more noise.
Now, muzzle brakes redirect the sound and sometimes make the heard sound worse depending on where the sound is redirected (back, to the sides etc...)
I hate the noise on my BM 16" with the AK type brake, and I hate the flash of my 16" SUM barrel with a crown finish.
All in all I now want 20".

Powder, cartridge case, bullet weight, barrel length to match requirements.
I was a combination of factors.

.223 burns the powder charge and reaches max pressure within 8" of barrel.  No powder "explodes" when it hits the air resulting in more pressure than was in the barrel.  Powder burns... it never explodes and the sound you hear is residual pressure escaping the barrel.  The flash does NOT cause the noise.  A Vortex does not reduce volume of escaping gas because its caused by pressure not flash.  The closer you get to the chamber the higher the pressure is in the barrel and the louder the muzzle report.  That said the muzzle brake is causing the problem with your rifle and removing it will solve the problem... you dont need a 20" barrel.

Purely subjective observation on barrel length/noise without muzzle brakes:

When I take my 16" carbine to the range, I often get comments from the shooters next to me about how loud they are. One has a Vortex FH.

When I take my 20" rifles, nobody ever complains.

Try a muzzle brake on the 20" and it will get louder than the 16" to nearby shooters.  Put one on a 16" and it sounds like a SBR upper.

like devl said, amount of noise is directly related to pressure and temp. when bullit exits bore. the higher the pressure and temps. of gas compared to atnosphere the louder the report. brakes direct it diffrently.

An ArmaLite 20 ith a brake is significantly louder than a 10.5.  Or at least more prone to causing a headache.