Do you reload? What is your current barrel twist rate? As DoyleAlley said, is the barrel shot out? What are you wanting to hunt?
If you reload, stay with that 260. If you need to re-barrel, go to a 1:8 twist if you don't already have that. You will be able to stabilize 140 grain bullets. There's not a whitetail on earth that you need more than that to kill. A 140gn Hornady SST over 43.5gn of Rel19 is death incarnate to deer and hogs out of my 260.
While you can assuredly shoot larger with a 308, you don't need it unless you plan to hunt large game like elk.
A 6.5mm bullet, weight for weight, is ballistically superior to a 308 bullet.