A .416 is a GREAT big bear rifle, however it's recoil for a factory ammo shooter is beyond what most guys can handle, accurately. If you handload, you can tailor ammo for whatever game you're after and load to whatever recoil level you are comfortable with. In a handloaded .416, a 300gr. bullet at 2,200fps makes for a very good bear/elk/moose load, yet is fairly pleasant to shoot.
: I know many fellows have .300's, but many of those I see at the range, have trouble with their .300's recoil, let alone something that has twice the felt recoil of their .300 as the .416 factory ammo has.
: A .375H&H will have perhaps 30% more felt recoil than the .300 - considerably less than the .416 developes. Some people, myself included, find the .375H&H generally more pleasant to shoot than a .300 mag. The .416Remingtons thump pretty hard in any standard rifle.