porting isnt designed to really reduce recoil. it will help with muzzle rise. A well designed muzzle brake will reduce muzzle rise and reduce felt recoil because its able to move the gases faster. my mossberg 930 is factory ported and is loud but i dont notice the recoil unless running 3" heavy shots.
Sorry schappellt, porting can and is designed to reduce felt recoil. A muzzle break is nothing more than porting added to the end of the barrel as opposed to cut into the existing barrel! True, some porting is designed to primarily reduce muzzle rise (like the magna-porting a magnum handgun), but other designs are meant to mitigate recoil. Depends on the design.
That being said, although schappellt alluded to it above when he mentions the speed of the gas, it really has to do with the pressure the given cartridge operates at. The higher the pressure, the more effective a break/port can be be.
Saami standard pressure for a 12 gauge is 11,500 PSI. The OP's 338 Win.Mag. operates at 64,000 PSI. Hence his statement to the effect that the porting does not seem to work on his shotgun, but works like a charm on his rifle.
From this we can conclude that porting of your average shotgun is a waste of time, while it might be much more effective on a high pressure rifle. With the shotgun, you get the added vectoring of the sound waves towards you with little reward in the recoil department, while at least with the rifle it makes a difference in the recoil.
All that being said, I would not shoot a ported 338 Win.Mag without ear protection, not even once while hunting!!!!!!!!!!!!
Read up on the science of noise damage to ears. I don't even think I would fire a shot from my AR without ear protection. I use sound cancelling electronic ear protection while hunting with my revolvers 100% of the time.
Therefor - I do not think it worth while putting permanent porting onto a high pressure rifle that is to be primarily used for hunting. Why bother? You don't feel the recoil while shooting at game and there are other ways to mitigate felt recoil while practicing on the range.