Depends on what you mean by better.
They are both cartridges made from the .308 Winchester case. The 7mm-08 is just the .308 Winchester necked down to 7mm, and the .260 Remington is just the .308 Winchester necked down to 6.5 mm.
If you mean which cartrdige is somewhat more powerful, with ammo that can be readily found, that is a fairly popular cartridge, that has been around for 15 years, that has been referred to by some knowledgeable gunwriters as the "perfect deer cartridge", for which many makes and models of rifles are still manufactured every year, then the answer is the 7mm-08.
If you mean the cartridge that is slightly less powerful, has slightly less recoil, uses a slightly lighter bullet, is slightly flatter shooting, was only introduced about 10 years ago and is already a total commercial failure, for which ammo is hard to find, and for which almost no rifles are made any more, then that would be the .260 Remington.
I'm not saying that the .260 is not, standing alone, a pretty good cartridge. (It is basically a souped up 6.5 Swedish Mauser). But, stacked up against the 7mm-08, that's how it stands.
Regards,
Mannyrock