WRT target shooting the little .260 is ballistically closer to the .300 Win Mag than to the .308 Win, not to mention that 6.5mm cartridges like the .260 are the ###y new thing in many target disciplines.
WRT hunting, both would meet your criteria.
Thanks to the department of idiocy at Remington, the .260 is for the most part a hand-loaders only proposition. They only chamber it in very few rifles and even then the twist is a little slow. People who like the caliber, like it a lot and generally snap them up when available.
Couple of points.
Rifle: If you want a general purpose rifle, then a .308 is available pretty much everywhere in pretty much every make, model and action. The .260 much, much less so.
Ammuntion: if you are buying vs. loading your own, same story. You are severely limited by the fact that only Remington and a couple of others load commercial .260 Rem.
Resale: Every FPS-playing, digi-cam wearing, mirror-posing fat kid wants a tacticool .308 (and a AR) and will be drooling all over your gun ####. The .260, less so.
However feel free to Google, .260 vs .308. I get about 88 million pages, which I'll let you read at your leisure.
PS. My favorite rifle for hunting up to deer size game is a Rem 700 Mtn in .260
