What Saggs said in the first post - the 300 BO round is not much different than a 762x39 round IMO, and the only reason I have one is to have a round that is versatile for using both suppressed and unsuppresed fire. It's really the best round out there for the AR platform now which allows you to do both well. If you don't care to suppress a rifle, you're not taking advantage of 1/2 of the benefit of 300BO, so 300BO is out on that score for the OP IMO. One thing to take into consideration is the magazine issue - 300BO you can use PMag and standard metal mags. 6.5G, not so much, so you'll need to get a separate stock of magazines for just one rifle, but considering the $ of mags, not a huge deal, but one to be brought up at least.
Travis Haley ran a 300BO rifle for an entire year on every course he taught and attended, if you check out his writings and videos on it, he probably has the most thorough explanations and valid opinions regarding all aspects of the practical uses of the 300BO round.
Considering the ranges brought up in the OP, the 6.5 is a better choice, as at mid to longer ranges it is typically superior to the 300BO, and the 6.8 as well. Plus with a 556 rifle with a 1/8 or 1/7 twist barrel set up for heavier bullets like the Mk262 or other 77gr/etc rounds, Maverick should have a pretty hard hitting rifle in that one for mid range already, so a 6.5 will give performance that'll push out a little further compared to that, where as a 300BO won't.