I just bought another .308 (had gotten out of them for a little while), but only really because I wanted a lightweight 16.5" barreled semi-auto, and the .308 was the the only chambering option for this rifle.
It sounds like you've made up your mind, but in your situation, I would go with the 6.5 all day and twice on Sunday. It's lighter recoiling, has superior external ballistics at all ranges, and is more than enough for any deer that ever walked at any range you'd use either for.
In my opinion, the sole upside to the .308 for most bolt gun uses is barrel life, but even then, it's really not much of a consideration for most people. I've got about 2,150 rds on one of my 6.5 barrels and it was still smoking clay pigeons at 700 and connecting with the steel torso at 1k just fine today. I'll probably replace that barrel after I burn up the last 300 or so 140 RDFs I have. I'm not really concerned about the barrel cost, I've spent a lot more on powder, cases, bullets (which are usually cheaper in 6.5mm than equivalent .308) etc, I'd rather pay a little extra for the higher performance than save a few cents in barrel life at the expense of everything else.
If you're wanting to learn to shoot for accuracy, cheapo steel cased junk shouldn't even be in the conversation.