If were up to me (and it's not....), I'd probably pick the 308 Win.
I have had both the 7mm Rem Mag and a 308 Win in 15" unbraked barrels. The 308 later became a 30-06 JDJ and I still have a 15" 7 mag barrel.
I've been rather disappointed so far in the 7 mag velocity. I think a 7-08 or similar would do nearly as good. However, it's been accurate with some loads.
The 7 mag recoil is probably my personal upper limit for a non-braked gun. It recoils more than the 30-06 JDJ does, and certainly much more than the 308 Win.
The 308 can be rechamber to several different calibers if you so choose to in the future, if you want more (30-06 AI, 30-06 JDJ, 30-284, 30-338, etc.), while the 7 mag doesn't give you any options, really.
In my own 308 barrel, I've gotten the ballistics listed below
150's @ just under 2600 fps
165's @ right at 2500 fps (165 BT's at 2484 fps)
180gr Remington factory ammo was clocked at 2422 fps (only 180's ever fired in it)
My 30-06 JDJ would do the following
150's @ 2850 fps
168's @ 2715 fps
180's @ 2550 fps (I didn't push them any faster - recoil was quite stout)
I have not really had the chance to ring out the 7 mag barrel as yet, but preliminary testing has shown only ~2600-2700 fps with 139-145 grain bullets, depending on powder choice.
Regards,
Rog