I've had at least one 264 win in the safe since 1995. Now I have four. They just plain work. I'm having another built currently to take full advantage of the 150-160g bullets. 264 Win is a fine cartridge, it has the advantage of a long history and Walmart available ammo that is capable of taking nearly anything in North America, within reason. As far as a long range hunter, it is my favorite chambering. 1,000 yards and in is certainly within reason. It is about as much powder as you can practically burn with a 0.264" bullet. There are other '26's' with more horsepower but the returns are really negligible for the amount of powder burnt, and barrel, and they aren't as easy to tame as the 264 Win. I don't see any practical reason for a 6.5-300, but if you dig it by ALL means run what what you like.
Not to muddy the water further but have you thought about something else? I would take a long look at a 6.5 Sherman as well. It runs on a standard 0.473 bolt face long action. They are efficient, don't run a belted case and run pretty well neck and neck with what a 264 Win is safely capable of, with better barrel life.
Just something to noodle on. Have fun.