I have nothing against the 7 STW, in fact I think it is a fine cartridge. I just don't see what all the hype is about. Ballistically it is very comparable to a 300 Win mag, just with a bit more velocity and slightly worse BC. Trajectory-wise at longer ranges it's a wash. The .300 having more frontal area will = more reliable expansion and it will retain more energy to drive that bigger bullet just as deep as the smaller 7mm.
I'm guessing the rifle the OP is asking about will be in the 12-14 lb range. With a brake on a rifle of that size recoil will not be a factor. If you're trying to save a little on the cost of components I can see going with a 7mm, but the .30 cals have better BC and more frontal area, along with generally better selection of bullets. And the 300 RUM will equal the velocity of the STW but using heavier, higher BC bullets. To me there is no advantage to the STW in this case except the cost of powder and bullets (which will be 10-15%). So I guess the question is whether you want better performance or cheaper ammo.
If we were talking about a light weight gun without a brake I would lean more toward the 7 STW since it can do pretty impressive things with 160-180 grain bullets.