The 120s in the .260 will probably out-penetrate the 130s in the .308, will definitely fly flatter and farther and will recoil less in the process. Those are the only advantages I can think of but no deer will ever recognize them. An elk might, though, but not much.
If you want to compare apples to apples, go with the 100gr 6.5 TTSX in your .260.
I have owned both and if you handload I'd run a .260 all day and twice on Sunday over a .308 for the recoil reduction alone. And if the two bullet choices are 120 in 6.5 and 130 in .308, that 120 is going to run flatter and get deeper for more icing on the cake.
