I've been shooting at 264 win mag for years now and really like the 6.5. It was a 300 win mag and I re-barreled it so I've kinda been down that road. I shot the 300 at everything, coyotes, crows, rocks, everything for several years and developed a flinch. When the barrel started to go on the 300 I had the 264 pipe put on and have never regretted it. It's a fairly heavy rifle I wasn't using for anything bigger than deer anyway. I started out using 140gr Accubonds and had good luck with them. I eventually started playing with the 140gr Bergers though and switched to them for this rifle. They shoot better past 450yds I found and I'm only using it for deer and antelope anyway, don't need a really stout bullet. I love the lack of recoil, I shoot this rifle really well, and the BC/velocity combo available with the 6.5's that burn some powder.
I eventually missed having a bigger magnum though and ended up with another 300 win mag, this time a lightweight 70 from Rifles Inc. It has a brake though, no more flinching! I like the power of the 300 with a stout 180gr bullet, mine is shooting Accubonds. I'd been thinking about doing this for some time and am glad I did. To me it's an ideal combination for the vast majority of my big game hunting. The 264 is great for antelope, whitetail, and flatter country muleys. The 300WM is great for steep country muleys, elk, and hopefully the moose I'll go chase next year. When I got my shot at the muley that was quartering away about as hard as one can be and still be quartering, I was confident in the big Accubond to make the kill at that angle and it did. To be fair though I took my biggest muley with the 264 and a 140gr Accubond at a similar angle. I'd have been leary of that shot with the Berger.
They overlap enough to be each other's back-up rifles on hunts too. This year I took both on my muley hunt and carried the 264 the first few days while hunting the plains part of the unit, the 300 when we struck out there and headed into the canyons.
I guess I'd consider what you other guns you have plus what you hunt and go from there. I can see a plus to both.