I don't own a 25-06 yet, but I have researched them a lot. The 7mm-08 Remington and the 25-06 are for all intents and purposes ballistic twins, that also produce the same recoil with the same bullets.
My thinking gives the 7mm-08 the edge because you can load heavier bullets than the 25-06, if you want to. In other words, the 7mm-08 can do everything the 25-06 can, plus more.
Don't mean to put down the 25-06, you should read some of the great elk hunting stories using the heaviest bullets.
FWIW