I'm not Brad, but a noted gunwriter that some have read on this forum seems to like the 140 TTSX in the 7mm-08 for elk, although at the modest muzzle velocity that cartridge produces, a 140gr Partition or nearly any well-constructed bullet should work well.
The cartridge is the least expensive item in your hunt. Don't be afraid of using premium bullets.
And, as others have mentioned, well broken-in boots, good binoculars and physical conditioning are far more important than the choice between a 7mm-08 and a 30-06 (which are both excellent choices).
