An issue is in the perception is not with the math, but how the sensor systems work. Human senses tend to work on a logarithmic scale and Decibels are a Ratiometric scale. If A is twice the size of B, then 3 dB = 10 LOG10 (A/B) which is 10 LOG10 (2). And "twice as loud" does not mean that the sound pressure is twice as high; it means that the Human PERCEPTION of the loudness is twice as high I think that this is because the cochlea is a logarithmic spiral. (But, I can be wrong and often am).
Back to the OP's Question. For years I hunted with an uncompensated Ruger 77 Frontier in 308 (16.5" barrel). I also have another bolt gun in 308 with a 22" barrel. In open air hunting and range situations, I don't recall the Frontier as being significantly louder. However, I certainly have no issue with the observations that a compensated semiauto 308 will be significantly louder with a 16" barrel. Also, I find that guns with Stoner semiauto actions are much louder than bolt guns (all of those moving parts).
However, this is a YMMV issue. For example, I have a Ruger Security 6 with a 6" barrel in 357 Magnum (uncompensated), and a Taurus 357 Magnum with a 4" barrel and a built-in compensation that is tilted slightly forward. I find the Ruger is significantly louder with full power 357 Magnum loads.