I have a Nomax 33 and like it a lot. Very good suppression and comfortable to shoot without hearing protection. Big, but surprisingly handy due to light weight.
I have shot 338LM through a Hybrid (mine), 36M and Rugged Alaskan 360 and none were comfortable to shoot, didn't really feel hearing safe to me.
I own a couple TBAC and am a fan boy, but don't have a 338 to compare the Nomax with.
I have been on the range with my Nomax 33 shooting 338LM with another shooter that had a TBAC and 338NM. We couldn't take ears off, but everyone was amazed how well they suppressed. The big cans are in a different class than the smaller cans with over bores IMO.
Recoil is more push and less snap with the can on, but I think about the same. I really like not having the noise of the break though.