It depends what your going to do.
For Elk and Moose I would say .300 is a better choice. 8mm or 338 as well.
For deer 7mm is fine. Not that you can't kill either with a 7mm but I would prefer 308-338 personally.
Stay away from the 7mm RUM. Heard some bad things about it. The 300 RUM or .338 RUM are great guns.
Personally I think these are overkill for most though. A 300 Win Mag or 300 WSM is more then sufficient for most. I like my WSM and have loaded and shot the 300 Win Mag quite a bit. Either one is a good choice. Personally I like the 24" barrel and short action with a little less recoil. In these barrel lengths velocities are just about the same. My buddy has a T3 Tikka in 300 Win Mag 24" barrel and loading both side by side, velocities are extremely close. Shooting out to 500 or 600 yards, these are great. I would probably think hard about taking a 500 yard shot, and I've probably shot 1500 rounds of .300, between two different WSMs and a 300 Win.
My question is who possess the shooting skill and practices enough to take the 600-800 yard shots at an Elk? If you think you can do that, you better be shooting enough to burn a barrel out in the .300 RUM.
Also, keep in mind 300 RUM recoil is about the same as 338 Win Mag. Which is also a great gun for elk and Moose.
Also, a 325 WSM is good choice. A lack of bullet selection is the only thing that would keep me from having one.