The 7-08 is one of the best, yet under-used and under-rated, deer rounds in existence, especially now with the plethora of great 7mm bullets to be had. It combines the best attributes of the short action .308, with the high BC and high sectional density of the 7mm.
It should make a great deer round to at least 400yds, and maybe even farther if you have the necessary skill to put the bullet where it needs to be. But I think for the "average" medium range hunter, 400yds is a good practical maximum with this round.
http://www.nosler.com/Bullets/Accubond.aspxsx
If you go to the link I pasted above, you can see the 140gr 7mm Accu-Bond has superior BC and sectional density to all but the 200gr .308 bullets. BC and SD are constant and don't dissipate on the way to the target like velocity and energy. They actually help retain energy downrange and deliver it on target.
Is the .270 a better round? Maybe, and it could be debated all day long as each round has much to recommend it. I feel the .280 is a much better round than the .270, yet it is largely unknown compared to the .270. They are both designed around the same parent case, the 30-06. Yet the .280 has a larger bullet selection, and also carries a larger bullet and delivers slightly superior velocity with a 140gr bullet.
Will the 7-08 kill Elk? Probably. Is it ideal for Elk out to 300yds? Not in my opinion, and it's not what I would carry on an Elk hunt if the ranges were expected to stretch past 200yds. But I do feel it will get the job done as long as ranges are kept sensible, probably 200yds and under. Yet it may even do the job out to 300, but it's not a shot I would take with either the .308 or 7-08.
Elk are rugged and the best way to stop one is to blow out both front shoulders. This takes a lot of horsepower, more than the 7-08 can deliver at much over maybe 100yds. I would carry something larger for Elk, even at short range. For 150yds and under, I would go .338 Federal. Anything over 150, and I would want a fast moving mag throwing heavy for caliber bullets. But I like to have a little extra HP on tap at all times, and I usually like larger bores and more power for most game than a lot of other guys. So my opinion on elk is just that, an opinion.
But if you want a combination rifle and will be careful o the shots you take on elk, than the 7-08 will be an excellent choice. It has enough for deer to 400yds, and will do the job on Elk to maybe 200. It's one of the better rounds to be had for a general purpose rifle, and only the .280 and 30-06 would be above it on my list of general use calibers.