This can start a good argument one way or the other on witch is the best rifle for hunting in the west.  My preference for elk in my .340 Weatherby loaded with a 185 gr bullet pushing 3400 fps.  Now as far as what will work on an elk or mule deer, it sounds like you have it covered.  The 7mm-08 is a fine round but I would load it up with a Barnes 140 gr bullet or even a 140 gr Nosler Partition and you would be set for an mule deer or an elk out to 300 yards and even 400 yards with no problems.  You have to figure that one of the great elk rounds is the 7mm Remington Mag shooting 150 or 165 grain bullets at around 3100 fps.  Even your .308 is a great elk and mulie rifle out to those ranges.

Now if you want a good excuse to buy a new rifle then any rifle in the .264 Whinchester Mag, 7mm Mag .270, .30-06, .300 magnums, .340 magnums, and to the .375 HH will do the job quite nicely. 

Now was that a lot of help? 

You sure know how to ask a question that can garner different responses from a LOT of people...LOL! Although most of my hunting has been in the eastern half of the U.S. I have been on a couple of western hunts in camps where both mule deer and elk were being hunted using horses. For the eastern U.S. I prefer something with a tad more frontal area and bullet heft than the 7/08. Oh, I own a 7/08 and have killed deer with that chambering, but my preferences lie to bigger bullets and very decisive kills.

Much of my time hunting in the eastern U.S. has been spent in very thick cover. I actually never killed any deer standing in a field for over 35 yrs after beginning deer hunting. I prefer a chambering that has a very good chance to drop a deer before it runs perhaps 50, 75, or 100+ yards and finding it (and then dragging it) becomes a bigger chore.

I have found that chamberings I've used on the north side of .30 cal kill more quickly and decisively than the .30s and those smaller. My choice is the next size up from the .308 parent case, the .338 Fed. Yours, of course is one size down from the parent case. At 300 yds, both with a 200yd zero, the .338 Fed falls 1.6" more than a 140gr/7mm08. (and also slightly less than a typical 180gr '06)

I carried two different rifles on my two trips out west, a Tikka in .300WSM and a Model Seven in  7mmSAUM. I preferred the rifle the 7 was chambered in as it was more compact and an easier carry slung across my back while riding. My choice today would be a BLR in .325WSM for elk, whitetails and mule deer. This rifle is not overly long and very slim sided so it could also easily ride smoothly in a rifle scabbard while riding.  

I seem to recall that you don't like recoil so if my recollection is correct, I'd say the .270 win.  It is a wonderful caliber with light recoil.  Mine is super accurate and a dream to shoot.  Some might question its ability to take elk, but I downed my 300 pound mountain goat with one shot.  Pancaked him right where he stood and lots of people have taken elk with the .270.

East:  My trusty 30-30 150gr HP, anything.

West:  I have faith in my 7mm Mag will

I too will choose my Marlin lever action 30-30 for the east coast.  All the hunting I do there is within 75-100 yards, and is in areas where a good brush gun is needed.

Out west, I have a Remington 700 BDL in 30-06, and I have not seen a reason to change. Standard Core-lokt ammo for deer, trophy bonded bear claw's for elk, and so-on.  I might need a different gun for lopes if get there some day, but it would probably be sufficient.

For the lower 48 a good East or West coast gun would be 270, 30-06, 7mm Mag (and a ton of cals in between those), all of which are good antelope to elk killers. If moving up to Ca or Alaska, maybe step up to the big 30's (mags) or 338 Mag for the big bears.

For me.....both rifles have very similar trajectories so the transition between the two is easy. Just my $0.02

East: 270 Win

West: 7mm Rem Mag

For whatever my opinion is worth I'd stick with the 7mm 08 for east and west. I've been using the 7mm 08 that last couple of years on both coasts with no problems. I also grew up out west and saw plenty of animals fall to rifles of similar stature. For once I'd love to take a guest out to the ranch who shows up with a sensible rifle like a 7mm 08 or a 308 rather than a monster magnum with an overcomplicated scope that causes more problems than could be imagined. All I can say is all of the wounded game I've tracked down has been from one of these and there's a reason the African nickname for Weatherby is "wound-er-by". For the record I've owned a handful of such weapons (300 win, 375, and 7mm) and some have been viable field pieces but also unnecessary as they buy little or nothing in terms of trajectory or killing power. And yes, the 7mm 08 will suffice finely for elk just like a 270 will. People have a certain amount of prejudice against short actions only because they don't realize that ballistically speaking they are producing the same result with less recoil. It's sort of a little festivus miracle so to speak but it's a mental barrier for some. 

P.S. Study your elk anatomy - the vitals tend to lie lower in the chest.

Highflyer, what on earth are you thinking, introducing logic and common sense into a discussion & debate such as this?  Suggesting that the 7-08 is perfectly adequate for both east & west hunting based solely on facts learned on the ground rather than theories removes the perceived need for getting a new gun.  As we all know, getting a new gun, regardless of caliber, action type, stock material, etc, is the goal of most sound thinking (?) hunters and shooters, self included.  Going to different time zones to hunt different species of game (or often the same species hiding behind a different kind of tree) requires if not demands a new weapon. 

That being said, here's no way my A-Bolt '06 would be adequate in New England hard woods or southern plantations.  In those areas, I would just have to get & use a .300WSM, possibly a semi auto to take advantage of that all important rapid second shot.

Then again, a .35 Remington out of a Marlin lever action might be needed for those big deep forest bucks in Maine, or maybe a.............