I think the biggest limiting factor will be the pressure at the gas port in a 6.5 or .260 barrel. I'd be comfortable going with an 18" or even 16" barrel as long as it has a rifle-length gas system. I'd hesitate to run a mid-length gas system in any 6.5/.260 barrel unless you have an adjustable gas block or carrier to reduce the violent cycling of the bolt.
Either way, the more aerodynamic bullets that you can use in 6.5/.260 calibers will be more aerodynamic than comparable .308 bullets regardless of how long your barrel is. But if you want a really handy AR, I'd consider a 12"-16" AR15 in 6.5 Grendel or 6mm ARC over a large frame gun. It just depends how much extra you're willing to pay for mobility on the large frame platforms.
For what it's worth, my 18" 6.5 Creedmoor comes in at about 12 pounds all kitted out with a full mag & 2.5-15x Ares BTR, whereas my 18" 6.5 Grendel is only 9 pounds with a mag & 3-15x SWFA. With a lighter barrel and optic, I could probably get the Creedmoor down to 10-11 lbs, but the Grendel could easily be under 8 with a lighter scope. Since Grendel covers the intermediate role so well, I don't mind the extra weight on the big frame gun to tame the recoil a bit better. With a 12" Grendel (or 6ARC), you save even more weight & size, while still maintaining the ability to hunt within ~300 yards and shoot targets out to 600+ yards very effectively.
For some people, a "mobile" gun could be 13 pounds, while others might not be happy with anything weighing more than 8 lbs. Just define the role you want it to fill, and build around those parameters. For me, the 6.5 Grendel hits the sweet spot, but the 6.5 Creed/.260 Rem definitely extend your range if you have the cash to spend -- and don't mind the extra weight.