Yes the 338 WSM is a great little round but it would be a waste of teh receiver length in the standard Rem 700. IT would work but why not just go with the Win Mag as it will feed better and give 100 fps more velocity.
I have an XP-100 handgun in the 338 WSM and it is a great round, in the 15" barrel I get 2900 fps with the 180 gr BT and 2700 with the 200 gr pills. Still, for the receiver being used, the Win mag would be a better fit, Hell, the 338 RUM would be a better fit as this would be easy to chamber in this receiver.
It is true, the 338 RUM will nearly match the Lapua in performance and the 338-300 RUM WILL match or slightly exceed it. Brass quality is not as high but in a sporter weight rifle for big game hunting it is plenty quality for fine accuracy and much less costly.
I'm getting +1000 yard consistancy with my Allen Mags using RUM brass so I am not overly concerned about the quality of the brass.
Good Shooting!!
Kirby Allen(50)