Well, it's always a barrel-burn vs. external ballistic performance tradeoff, with a few minor variables thrown in (factory offerings vs. cost of custom, etc.)
On the very high end
-New Nosler round - .26 Nosler
-.264 Win mag
I wouldn't do either of those, and espec. not the .264 win mag - worst of all worlds - rapid throat erosion and a belted case.
In the high range,
-6.5mm-'06 A-square
-6.5mm - .284 Norma
I rank both of these pretty highly, if you're not shooting a TON. The 6.5mm-'06 offers a little more performance but in a long action. However, on the other hand, if you want to use the longest bullets in 6.5-.284 , you may have to use a long action anyway, so why not get the better performance from the 6.5mm-'06 if you're going to use those super-long bullets?
In the mid-high range,
-6.5x55 swede
-.260 rem AI
-.260 rem
I think all of these are good - the 6.5x55 has gotten so popular in the last 5 years, that there are no less than three factory offerings at Academy sports - so it's arguably the #1 best tradeoff / choice for the average hunter. It's usually in a long action. Also, as someone mentioned, since 6.5x55 rifles are usually made with an 8.0 twist, rather than 8.5 or 9 like others, if for some reason you just wanted to hunted some very very large tough game like big bears, large african plains game, etc., with this particular rifle (I wouldn't but you might), the really heavy & long 160/162 will work in them (although in fairness, such bullets have a round nose and flat base, so they'll still probably work in 8.5 to 9 twists, too, so this could be a false advantage). The .260 rem AI would be the "best" choice for most people if it wasn't still a wildcat (hasn't come into its own as a mainstream ackley chambering like the .280 rem AI has, unfortunately)... you get the performance of the hot-loaded 6.5x55, but still in a short action. You can shoot .260 ammo in .260 AI chambers of course, as with all Ackleys.
Then the 'smaller' ones (6.5 creedmoor, 6.5x47), and then the little 6.5 grendel. In a bolt action...just say no to these, in my opinion. In an AR15, 6.5 grendel is ok. In an AR10, 6.5 creedmoor is ok, but still .260 is definitely the best choice for a turnbolt and arguably for an AR10 too. Cheaper, more performance, etc., than the creedmore or 6.5x47mm. No downside except the shorter neck, but that doesn't matter unless you're trying to squeeze benchrest accuracy and using the longest possible bullet.
So...
For the rich hunter with plenty of money to re-barrel ==> .26 Nosler
For the hunter who wants a canyon crosser but won't shoot all that much ==> 6.5mm-'06
For the hunter who wants same but shoots up to maybe a couple hundred rounds a year ==> 6.5-.284
For the nostalgic and/or someone who wants readily-available ammo ==> 6.5x55 swede
For the practical shooter or hunter who shoots upwards of 400-500 rounds a year ==>.260 or .260 AI.
For someone trying to squeeze out a 0.2 MOA gun rather than a 0.3 MOA gun and obtain a multi-thousand round bbl life, ==> 6.5x47 due to the longer neck to hold the longest bullets in the most perfectly straight, symmetrical manner.
For an AR10, ==> 6.5 creedmoor or .260 rem.
For an AR15 ==> 6.5 grendel.
It's all good, as the kids say.
Personally, the custom rifles I take a closer gander at for hunting, when they come up for sale, are those in 6.5mm-'06 and 6.5-.284. The rifles in European styling (Mannlicher and/or schnabel forends, Euro buttstock), such as the Sako Bavarians and CZ 550 FS, I get more excited by the 6.5x55... but then again, that's the only chambering in 6.5mm that they're offered in.
Having said that, I'm mulling over the idea of getting enough $$ together to do a just-one ultimate hunter turnbolt in .260 rem AI to replace a .280 rem for tough terrain hunting. But if I'm gonna spend several thousand for a custom CF-wrapped bbl, I want said bbl to last, and this seems like about the best tradeoff in bbl burn vs. performance, to last the rest of my lifetime of hunts.