The military made the move to the .300WM as a mission based option some time ago in their sniper weapons. I wouldn't use that as any kind of deciding factor on anything though.
I have a .308. Shot it Friday, in fact. It shoots very well. It's a Savage action from a rifle that I bought at Wal-Mart for $397, an ER Shaw prefit 20" threaded barrel from Midway for $139, a Bennie Cooley muzzle brake from Brownell's for $97, all installed in a PDC Custom aluminum chassis (way more than I *needed* to spend on a stock). Performed all the work myself.
Shot at 100yds with handloads. I'm happy that I didn't yank one of them. Best group of the day at right around 0.67". The other 3 I shot at that range were right at 1".
Same load at 300yds. This group was 1.6" The wind was really starting to blow and swirl and the mirage was terrible. The other 2 groups I shot at 300 were right at 2.7".
It shoots great but I don't like shooting it that much simply because of the price of .30cal bullets worth shooting. I fired 35 rounds on Friday and while considerably cheaper than shooting factory ammo, it was still nearly $10 in components not counting brass. In contrast I can shoot 100 rounds of .223 or .243 for $20. Additionally, neither the .223 or .243 need a muzzle brake to be all day shootable.
The first of my 2 hunting rifles is a Savage .243 that my folks gave me for Christmas in college. It began life with iron sights and the original factory barrel was scary accurate with everything I ever fed it. Almost the point of being boring, in fact. Load development was really a matter of how much effort and components do I want to spend finding that fraction of an inch? I installed the .308 sporter barrel from the rifle discussed above for a bit and decided that I didn't want to deal with the additional recoil and expense of practicing with it and went back to .243 with another factory barrel that came off the action my long range .243 is built on. I haven't shot it with the new barrel yet. If it isn't a shooter, I still have the original barrel laying around. It isn't pretty, what with the holes where the irons used to be, but the results from it sure are. Why all the barrel swapping when I had a factory .308 and .243 in my hands? I'm left handed, my long range bench/bipod guns are right handed and my hunting rifles, like this one, are left-handed actions.
My second hunting rifle just arrived earlier this last week. After an exhaustive search for what I wanted, starting with Savage (they made the rifle I was looking for for 1-2 years but it isn't a current model and finding one for sale is rarer than hen's teeth) I ended up discovering that only Browning and Winchester currently chamber rifles in 7mmWSM and only Browning makes them with a left-handed action in several models of both the A-bolt and X-bolt. Mine is an X-bolt Hunter. I looked at the Medallion but I don't do "shiny" on hunting rifles. I'm still waiting on the scope bases and the scope, both of which have been on backorder since mid Feb.
Where am I going with this? I don't particularly like the .30 cal cartridges for long range work. The .308 in particular is underwhelming in what it offers and I have one that shoots great. The 6mm cartridges offer better ballistics for long range shooting; you have to step up to a .300 Win Mag shooting heavy bullets (with heavy recoil) to keep pace with a .243 shooting 105-107gn bullets with regard to bullet drop and wind drift. The 6.5mm offerings up the recoil slightly but bring more energy to the equation and the availability of higher BC bullets than the 6mm. The combination extends the hunting range a good bit. The 7mm's, especially the 7mm magnums, offer even more efficient bullets, flatter trajectories and lower wind drift than most anything, better energy retention than the .300 Win Mag and with a recoil level right around that of a .30-06.