AL, I've had 308's with 18.5, 19, 20, 22 and 24" barrels. It's one of my favorite rounds (grin).
A 22" 338 WM is a lot louder than a 308 in any of the barrel lengths I just listed. Trust me on that. The 338 burns a heck of a lot more powder and the noise from that combustion is going to go somewhere...