There is a great deal of difference in recoil perceptions not only from person to person but more importantly in how and where the rifle in question is being shot. None of the three mentioned are supposed to be shot very much from the bench although testing of ammo and sights etc, requires at least a few sessions. From sticks or offhand the 375 is a bit sharper but the 404 and 416 are by no means difficult to master. The 404 with a 400gn at 2350 is what the 416 was loaded to, so in similar 9 1/2 lb rifles there will be similar recoil. Any shooting that requires multiple shots when away from the range (that is in a hunting situation) are of no consequence as concentration is on the animal, or animals that you are hunting. Multiple shots at the range if taken with a purpose in mind such as seeing how quickly you can reload and keep your shots on a 8in (200mm) square steel plate at 55yds or so, also keeps the concentration off the recoil so that it not only becomes manageble but familiar.
These are still in the sensible range of rifle cartridges and designed when results and managability were the taking over from the VERY heavy recoiling black powder bore rifles.
Now it seems the trend is for 50, 60, and 70 cal cartridges as ego and disposable income increase in some sectors.
The fact remains that the 375, 404 and 416 range of cartridges are about the best ever bought to the market in terms of managability for the hunter and effectiveness on the big animals, and the smaller ones for that matter with all three more than capable out to 250 - 300 yds if need be. They are all easily handled by the average hunter with a little practice away from the bench. It is also a good idea to have a lower velocity load to practice with. I have had a mold made that drops a 350gn cast bullet that I GC and load to 1900fps for plinking and 2365 for recoil and recovery practice.
Von Gruff.