This is a splitting hairs sort of choise I shot 308 for may years (my first gun was a Isralli converted k98) I shot everything from fox to bears. To be honest I would be hard pressed to find a practical difference between them. 308 has the edge energy wise but 7-08 has the edge ballistically. but in both cases the edge is slim.
As a deer/bear gun oth would serve you well I give the 308 a nudge for the bigger stuff and the same difference for 7-08 on the varmint side.
I don't think I could improve on that comparison of these 2 fine rounds.
That being said & we know that both rounds will do the job, let's
look at the economic factors.
If you look at factory ammo, the cost for new ammo coming out of the factories will be similar, but in out of the way places you
can find old 308 ammo on the shelf at lower prices. For ammo just to shoot paper, bust rocks, just to shoot, you can get 308 Mil, not so with 7-08.
When it comes to reloads, the cost diff. between say 140gr. 7mm bullets & 150gr. 308 bullets is very small & you use the same primers & allmost the same amt. of powder. But you can get cheap 308 brass all day long if you look for it. Sitting right beside my computer is a box of 7.62 brass that an old Warrior gave me. When it comes to brass, there is no comparison & even with non-mil. brass you can go to powdervalleyinc.com & get a super deal.
When it comes to info about the 308, go to 6mmbr.com/308Win.html & you can stay busy there for awhile.
For your situation I believe the 308 would be hard to beat.