For Whitetails and Mulies in Montana, I would probably go with the .25-06. Loaded with something in the 110-120gr range, you still get great velocities, great range, and plenty of retained poop to knock over any buck at a reasonable range. My dad and brother have used the .25-06 almost exclusively on Mulies and have never had any problems. My brother has taken several cow elk with his using 120gr Partitions. (he has a bigger, badder, boy for taking after the bull elk, but that's a different thread) A major attraction for the 7mm-08 would be that it is short enough to not require a long action, so you have a slightly greater choice of rifles available. The short action also means a little less weight if you are packing it around in the mountains. If all your shots are going to be inside of 300 yards, I am sure no Mulie or Whitetail will know (or care about) the difference between the two.
It is almost like the question about which is better, the .270 or the .280 Both are fine choices. Either one will do the job. If you already have a .25-06, go with the 7mm-08. If you don't, flip a coin.