I now use a 7.08 for Moose (use a 243 for deer).
I used to hunt everything with a 30.06, then the kids moved out and I could afford some new rifles
A 30.06 produces somewhere between 18 to 20 pounds of recoil (depending on rifle weight, bullet weight etc).
A 7.08 produces somewhere in the 12 or 13 pounds of recoil range (same variables) - so barely over half the recoil.
It is "noticeably" easier on the shoulder than a 30.06 - if I shot a 5 shot group with my 30.06 my "shoulder" knew it. I can shoot 40 rounds with the 7.08 and my shoulder is "just starting to notice".
I did buy a new rifle (ok, couple years back). I bought a Weatherby Vanguard II Sporter (wood stock) chambered in 7.08 and glassed it with a Burris E1 3-9X40 scope.
The rifle is "heavier" right out of the box and with the scope and rings, sling and the magazine full it comes in a little over 9 lbs - being heavier knocks the recoil down even further. That may be an issue for some, but where I "hunt this rifle" I'm not humping up and down hills, much less mountains. It spends a great deal of time "sitting on a watch" with me.
Like I said, I use the 7.08 "exclusively" for moose (eastern moose in Northern Ontario, not Yukon/Northern BC moose - I say that because some would say there is a difference and it sounds like "out west" longer shots are more common - most places I hunt in Northern Ontario you can't see further than 100 yards or so due to forest density).
It is a viable moose caliber out to way past where I would shoot (it's easily a 300 yard gun). I load it with 140 grain Swift A-Frames (my go to moose bullet) or alternately I would consider a 140 grain Nosler Partition or Accubond as "just as lethal" - my rifle seems to like 140 grain bullets. And I do advocate using a fairly stout bullet in a sub-caliber or (in the opinion of some) a "marginal caliber".
With a 7.08 if used in the same sentence as Moose I would "absolutely avoid" any mono bullets (E-Tip, TTSX, GMX). A 7.08 barely has the muzzle velocity to get good expansion from the mono's (much less out at 200 or 300 yards), so if you have to shoot copper, this is not a caliber for you unless you are shooting deer at 50 or 75 yards.