I got a .260 Remington rifle four years ago. A few trips to the range and it's all I've carried into the woods for the past four years. It has light recoil (I use 140gr bullets because I like heavy for game bullets) and is flat deadly on deer (all I've used it on besides paper so far) with none I've shot running over 30yds from where I shot it, none have left my sight. I use simple factory loaded 140gr Core-Lokts. Entrance wounds are .264" and exits are about the size of a nickel. I've never recovered a bullet and once it went through both shoulders and the near side leg bone. Using 120gr bullets, it's up near 2950fps. The 140s are around 2750fps and shoot a little flatter than 180gr in .30-06 using just Core-Lokts in both.
I have both .30-06 and .270Win rifles and none of those have been into the woods with me since I got my .260.
If you get into long range shooting, to equal the BC of the 140s in 6.5mm you have to go to around 168gr in 7mm and 190gr+ in .30cal... both corresponding to more recoil to get the same MV. Of course, .338" has some really insane BC bullets (the new 300gr Accubond has a BC of over .700! and the 300gr match bullets are 1.0+!) but you're talking some serious recoil to get those out at 2700+fps MV.
As far as comparing the .260 to the .308 at 1000yds, "The Monograph" paper said that the 6.5 Grendel penetrated at 1000yds better than the 7.62x51 and the .260 is the big brother to the 6.5 Grendel (roughly 300fps faster with 120gr bullets) (here's that paper: http://www.dtic.mil/cgi-bin/GetTRDoc...f&AD=ADA512331
the 'alternate calibers' part starts around page 30)