I've got both. Each rifle though both are Rem. Mod-7, have different personalities.
The 7mm08 definitely has a bit more "horse power" when it comes to taking down deer, but dead is dead. The .260 is no slouch and is a bit more accurate than the 7mm08 (different personalities as I said).
For deer, it makes no difference. Advantage goes to the 7mm08 for ammo availability and availability of loading components on most LGS shelves.
If I was to get a new 7mm08 I'd look at the Savage or Marlins on the budget end, a Tikka for mid-value, and a Forbes Light Rifle or Kimber on the upper end.
My Remington Mod'7's have a few "issues" and for the price aren't that good of a value. Both required working of the trigger, and both have been free-floated and glass bedded. The .260 suffers from an insane 1/10" twist barrel which makes is very fickle about boat-tail spitzers over 120gr. (Yes, thats right! a 1/10" twist!). But, with 120gr bullets it's a sub-moa tack-driver. I've gotten good groups (at or just under moa) with 140gr Spitzer flat-base bullets (Speer and Hornady) and same with 160gr Sierra RN (discontinued).
I really like both rifles and especially consider the 7mm08 a "keeper" as it has killed a train-car load of game in it's short life (attained in 2004). I consider it a 2moa rifle, but It kills far beyond expectations. The fact that the short 20"bbl gets published velocities for 24" bbls is it's standout point... I originally planned to rebarrel it to .284wcf but quickly decided against such after chronographing both factory and reloaded ammo. It easily attains 2,900fps with 139-140gr bullets.
The biggest advantage the 7mm08 has over the .260 is that the 140gr bullets (and most other "same weight" comparisons) the 7mm08 will be between 100 and 200fps faster. Certainly an advantage in the game fields. When comparing such bullets as the 160gr Sierra GameKing and Nosler Partition to the eqivalent 140gr in the .260, the 7mm08 holds the advantage in weigh and diameter with equal b.c. and s.d. Though neither have much recoil, the recoil of the .260 is just a tad less than the 7mm08 but you have to shoot them side-by-side to really notice a difference.
Given the expense of an elk tag and trip to the western U.S., I don't consider either first choices for elk, but, my 7mm08 HAS taken an elk... by a friend in '06. I probably won't be taking mine west this November. Most likely the .300RUM and either .30/06 or .338ME. Even the .257wbymag nor .270 won't make the "cut" this time.
fwiw; you can form .260 brass from .243 or 7mm08 brass, and .308, too but it's more difficult. btw; I don't own any head-stamped .260. It's all been formed from .243wcf.