The 308 and 6.5 creedmoor were/are both used a lot for long range competitions .. so lets talk long range..

Excerpt from an article I read..

My definition of long range is the same as the NRA’s—800 to 1,200 yards.

Using the excellent Berger Bullets Ballistics Calculator, let us compare a 140-grain Berger VLD bullet (MV 2,650 fps, G7 BC, .304) from a 6.5CM, at 1,000 yards, with a .308.

Long Range 6.5 CM Ballistics
Velocity: 1,370 fps.
Bullet drop: 348.59"
Wind drift, 5 mph from 9 o'clock: 39.18"

Long Range .308 Ballistics (175-grain Long Range BT, G7 BC, .262, MV 2,650 fps):
Velocity: 1,203 fps
Bullet drop: 386"
Wind drift, 5 mph from 9 o'clock: 48.53"

That's almost a foot more in wind drift and over 3 feet more in drop for the .308.. that, is substantial...

Winner: The 6.5CM

As to using the 6.5 on elk, which in my opinion are tougher than moose .. I have had no issue using a 6.5 and dropping them from 250-600+ --and that was using 140gr Nosler Accubonds.. basically an updated version of the partition as the weight retentions are very similar.. ..

This was opening morning a few years back--264Win --140gr Accubonds.. 430 yards.. 1 shot..

20121020_081239 by A Hoffart, on Flickr

They BOTH will work.. My wife using her Kimber in .308 also using accubonds... 355 yards quartering away..

DSC01329 by A Hoffart, on Flickr

If an animal can't breathe they will die..bullet selection and placement are key.. the author above states how the 6.5 is so much easier to use in terms of recoil and ability to shoot accurately..I'll take that...

Excerpt from article

"All things considered, the 6.5 Creedmoor is a cartridge that helps maximize the shooting abilities and maximum effective range of the hunter to a greater extent than the .308 Winchester. Proper shot placement is extremely important when it comes to ethically taking game and the aforementioned strengths of the 6.5 Creedmoor all facilitate precise shot placement. Finally, the high SD bullets used by the 6.5 Creedmoor also assist with penetration to help the cartridge “punch above its weight” in a manner similar to the 7x57mm or 9.3x62mm Mauser cartridges."

The 6.5x55 seems to do just fine on moose in Sweden ..