A dedicated rimfire can would almost certainly be quieter than a .223 can on a .22LR, but rifles with subs are already quiet and so you may not notice a huge difference (other than first round pop, which is probably kinda bad on that big centerfire can).
Obviously, you can easily test this theory by pulling the TBAC Takedown off your pistol and temporarily swapping it to the rifle, but if what you're really looking for is encouragement to buy another rimfire can, I'll be happy to endorse this concept
I've really been digging the Oculus22 lately - the modularity is kinda cool (run it in the "long" config for range sessions, and "short" for wandering around the property), and it's all stainless so no worries while cleaning. But if you bought another TBAC Takedown or a Dead Air Mask then you're also making a sound purchase. Err, no pun intended.