I have shot cow elk and mule deer with a 6.5 CM and it worked just fine. I would say it fulfills the same role as a .308 Winchester in the tasks department. It has better windage and trajectory slightly.
Either will work just fine. The 6.8 will carry energy out a bit further but for 500 yards and closer, the 25-06 shoots flat. I can honestly say that most of my mule deer shots have occurred at 200 yards or less with a few that were farther.
It depends on the market. As is the .270 Winchester in its current guise will fulfill the majority of hunters needs just fine. If people go crazy for it, it may happen. For people shooting 400 yards or less, it won't make a bit of difference.
There is truth to the fact that there is a point of diminishing returns. There is quite a bit of difference between a projectile that weighs 0.35 grains going 250 fps and a bullet weighing 180 grains going 250 fps, however. I do believe the 7mm Remington Magnum is one of the greatest cartridges...
The 6,5 Creedmoor was designed specifically to match the .260 Remington in performance yet allow the cartridge to be loaded into an AR10 size magazine without sacrificing case capacity with the typical 140 grain bullets of today for the caliber. It does that.
Love my 257 Weatherby for 500 yards and in for medium-sized game. If I were after elk or bigger, I would probably go 7mm or 30 caliber magnum cartridges.
I myself with that cartridge and the distances you specified would go for a 180 grain projectile. Either a 180 grain Accubond by Nosler or a 175 grain LRX by Barnes. Nice thing about 30-06 is that most bullets are designed around its performance so you actually have quite a few choices.
I find it is shot placement first of all. Bullet selection also has some merit as well. I have notice cartridges with higher velocities tend to turn the switch quicker in most cases.