The medium case capacity 6.5s represent the smallest cartridges that I consider appropriate for use as general purpose big game rounds; the 6.5s shine in the role of mice to moose cartridges. They're appropriate for use on all North American game with the exception of Woods Bison, only because minimum cartridge limitations are imposed in the Yukon. I would not feel the least bit unarmed with a 6.5 loaded with tough 160 gr bullets for bear protection, regardless of species, provided I was travelling alone.
The quarter bore guys tend to fuss when I say that general purpose big game cartridges start with the 6.5's, as there is such little difference in bullet diameter between the two. But the advantage the 6.5s have over the .257 is not the meager .007" difference in bullet diameter, but in the 6.5's broad selection of bullets. With game bullet weights up to 160 grs, the 6.5s overshadow the .25s by a considerable margin. Admittedly the introduction of lightweight premium .257" slugs reduces the disparity between the two a bit, but not enough to influence my point of view. It should be remembered that cartridge preference is almost always based on opinion rather than on hard fact.
Their moderate powder capacity allows 6.5 rifles to be a bit shorter and lighter without giving up critical performance. A small, short rifle chambered for a moderate 6.5 cartridge neither increases blast or recoil in any important way compared to when chambered in larger rifles, which cannot be said for larger cartridges. The mild blast and recoil from these rifles benefits field marksmanship, and results in a greater rate of success than simply choosing a cartridge based on energy figures from a ballistics table. For some reason 6.5 rifles tend to be far more accurate out of the box than some of their larger brothers, and are far more accurate than can be exploited under typical big game hunting conditions by the majority of hunters. Trajectory, when a slippery bullet is chosen, allows a competent field marksman to make quarter mile hits with his 6.5, without having to crank on his scope's elevation adjustment. If it wasn't for a 45 year love affair with the .30/06, the 6.5X55 might well be my darling, although the 6.5X55 is but one of many similar cartridges.
While slightly more capable, the .264 Winchester and the new .26 Nosler require larger rifles, and longer barrels, to exploit their advantage. These cartridges have the ballistic advantage to be excellent choices for the long range marksman, they don't share the moderate 6.5's primary advantages of mild manners in a conveniently sized package.