Ruger M77 is what it is. Wondering what difference it would make? I understand the difference in the ammo, but why would it matter when it comes the the model of the rifle? Just asking.
It makes a difference in how you are going to use the rifle. Just saying a Ruger M77 could mean anything from a Creedmore model to a scout rifle. One is for long range and good for that set up and long range shot and the other is for walking in heavy woods or rough terrain and is for getting up to your shoulder for a quick shot.
Saying .338 leaves it open for:
.338 Federal
.338 Lapua Magnum
.338 Marlin express
.338 Remington Ultra Magnum
.338 Ruger Compact Magnum
.338 Sabi
.338 Winchester Magnum
.338-06 A-Square
.338-06 Ackley Improved
.338-378 Weatherby Magnum
I am a .338 Federal fan, it doesn't beat you to death, has a lot of power is accurate and has an 8" drop at 300 yards. I would keep my shots at or under 100 yards.
You could use a .338 Lapua and take the beating but you can shoot your bear out to 600 yards.
You could have the .338 Weatherby, knock the snot out of you and an elephant at 600 yards but it costs $154 a box.
I'm not trying to be a wiseguy but knowing what you are shooting makes a difference.
Either way you got a great scope, I was just trying to steer you to a size that would be easier to carry for long periods in inclement weather and rough terrain and be suitable for your game. If you are young and stout and in great shape it might not make as much difference to you but when your bones get a little creaky and your legs get tired faster than they used to little details like that become important.
Good luck with the hunt and don't forget to post pictures.