The 7mm has some of the highest BC's out there but your chunkin a big peice of copper out there thats going to go on down range after the hit or miss.
I won't argue the advantages of 7mm bore, but the problem with 7mm-08 is that 1) being chambered in short action guns for the most part, bullets over 150 gr. don't work especially well and 2) The 7mm-08 can't push the heavies fast enough to take advantage of their high BC's (as well, BC often falls off as velocity decreases.
Now .280 Rem. vs. .25-06 changes the game a bit, but if deer are to be your largest game, I still give the .25-06 the nod. Despite the grumbling about .257" bullets, there are several in .400 to .500 range, which isn't much below the .248" pills the 7mm-08 can handle. And the higher velocity of the .25-06 gives it the advantage in trajectory to . I have pushed 117's to 3,227 FPS and 100's to 3,585 FPS without pierced primers or sticky extraction. And that's from a 24" Rem. 700.
This is using published data for max velocity for 24" tubes:
.25-06, 115 gr. Berger VLD, 3,100 FPS MV, 200 yard zero:
@ 500 yards:
Drop: 33.3
Velocity: 2,313
Energy: 1,366
Time of flight: 0.560 sec.
Drop: 234.1"
Velocity: 1,653
Energy: 698
Time of flight: 1.328 sec.
7mm-08 Rem, 140 gr. Berger VLD, 2,900 FPS MV, 200 yard zero:
@ 500 yards:
Drop: 37.6"
Velocity: 2,206
Energy: 1,513
Time of flight: .593 sec.
@ 1,000 yards:
Drop: 258.5"
Velocity: 1,616
Energy: 812
Time of flight: 1.388 sec.
As you can see, the difference in energy remains insignificant (about 160 FPE muzzle, about 110 FPE at 1,000 yards). But even with a lower BC, the .25-06 will have less drop and a shorter flight time, regardless of range. It's not much of a difference, truly, as long shots with any rifle require accurate ranging and knowing your ballistics table like you know your own face. But a longer MPBR is always nice.
My own 117 gr. handloads averaging 3,195 FPS are only 32.5" low @ 500, despite the lower (.410) BC of the Sierra 117 gr. Gameking. My 100 gr. 3585 FPS Barnes TSX-BT load only drops 27.1" at 500 and retains 1,517 FPE.
For the OP's purposes, I think the .25-06 is probably the better choice, if only by a small margin. It's not quite as efficient as the 7mm-08, and the difference in recoil is negligeable, but rifle choices, ammo availability and ammo cost favors the .25-06, and for varminting, the .25-06 is just plain superior. 75 gr. bullets at 3,700 or 3,800 FPS make a wonderful mess of vermin. This I know