How about a .300 WSM?
haha
I wish the 7mm RM and .338WM weren't shorter than the .300win.mag., man it really bothers me!
I'd shoot 160gr with the 7mm, 180 with the .300, but the 7mm with 175gr have such high SD's, either or could probably take anything in NA.
You said you were sensitive to recoil, maybe get the 7mm RM.
What are you planning to hunt anyway? mostly? if it was mostly deer and maybe an elk or moose one day, I'd say maybe just get the 7mm.
If you were gonna mostly do elk, and the occasional deer I may say get the .300 win.mag.
Is this going to be your 1 gun for everything?
Do you have a .270win or something? if so that may change things...