As stated earlier either is fine.
The 7 mag will have slightly less recoil, if you are recoil sensitive it has a pretty good kick, and if you don't like it you will hate the 300 win.
If you are recoil sensitive go with the .280 or 30-06 the animals won't know the difference until the range gets well past 200 yards.
If you are OK with recoil toss a coin, either is an excellent caliber.
My personal preference is the .300 Win with 200gr Partitions for elk.
I had a mercury recoil suppressor installed in the stock which greatly reduced the recoil.