On a short action the 6.5 gives you more of the good things and less of the bad things. 308 is still a great round with a ton of options as well. Inside 300yds it's kind of a wash, so distance would show where others shine over one another, but if you are a bench/LR shooter, we don't have to explain ballistics to you, you can probably school us. I have bigger/heavier rifles but like to grab a sub 8lb rifle in .270/.308/6.5/6mm when I head out. Options are great. I think getting a good lightweight, balanced rifle is more important than caliber.
Best of luck!
Best of luck!