Re: .308 or .7mm-08
Well their both based on the same case so the powder charge is gonna be about the exact same.
Accuracy , well that all boild down to the gun and loads more than the caliber both are ready to shoot better than you can handle the gun if the weapon is built right and the loads have been worked up properly. As far as accurate factory ammo then that I believe is gonna go to the 308 due to the numerous factory "match" ammo out their.
Recoil , well that all boils down to the math , shooting the same bullet weight with the same powder capacity and powders of the same or close to the same burn rate is gonna give you recoil that is about identical , assuming that the guns are the exact same shape and weight. Now once you get into the heavier bullets that the 308 can handle then the recoil is going to increase.
BUT , you can push a 150gr bullet out of a 308 alot faster than a 7-08 because on the weight to gas space ratio , the larger bore burns the powder faster and more effeciently.
NOW , for the other side , the 7mm bullets are going to have a higher BC than the 30 cals until you get into the heavier bullets and then the 308 will start to strugle with pushing them well.
Personaly I like the 308 , you can get great factory ammo from BlackHills (175gr MatchKings) and if you rig is ready and up to it you can be making 1000yd shots , where you'll be hard pressed to find any factory ammo for the 7-08 that'll be willing to reach out much past 600yds.
the differance in recoil is not going to be enough to matter.
Are you looking to have a gun built or buy a new one , what are you planing to use this rig for?