For the ranges you're looking at either would be fine. I've never had a 6.8, but most who have them seem to like them.
I recently built a .243, and to date it's my favorite AR. With the right parts you can make them acceptably light, mine is 9.75 lb WITH a 4.5-14x Zeiss and empty mag, but still not as light as the smaller platform though. I used a 22" barrel to keep the performance up. I've had a 25 wssm in the AR platform, and the performance was very impressive, 200 to 300 fps faster with any bullet weight than a 243 win. But for reasons of brass and fickle reloading traits I probably wouldn't go there again.
Another good option would be the 308. You could get a shorter barrel to save weight and not lose quite as much performance as you would with a short 243.