There's enough variety in 7-08 out there for about anything you'd wanna do with it. It is lighter on your shoulder and carries as much punch with a better ballistic coefficient (will shoot a little flatter and carry a little more velocity out farther) as its .308 parent. I like the .308, though, but I mean, if I couldn't have found my M7 in anything, but 7-08, I'd have gotten the 7-08. I really like the 7mm bullet size for the excellent BCs and sectional densities, yet carry more weight than the .264" stuff (.260 Remington). I own a 7mm Remington Magnum and had a 7x57 Mauser for a while. So, look around at your local ammo sources for what you can get in 7-08. No doubt, you can get more variety in .308, I mean, if you can find .308 anywhere right now. At this time, for political reasons, there is a shortage of especially military caliber ammunition. 7-08 is a very capable caliber and IS a little softer shooting than .308 in a lighter gun.
I handload and appreciate the variety of 7mm bullets for reloading, too, as good as in 30 caliber now days. That wasn't always the case in my lifetime, but it is now days. A 7-08 will do anything the .308 or the 270 can do from deer to elk with an appropriate bullet. Most calibers are that way, though. What can a 7 mag do that a .30-06 or .308 can't? Nothing. Might give you 50 yards more point blank range before you have to bother with hold over, but that's about it. What can the .270 do that a .280 Remington, a .308, a 6.5x55mm Swede, an 8x57, a 7x57.....well, you get the point. They're all good calibers and all kill the same game just as dead. The only reason .308 and .30-06 are so popular is that they are/were military rounds. The firearms manufacturers, over the years, have always had to come up with "something better" for gun sales and that's why there are so danged many caliber choices around. Some are long gone, some are fading as I type this, but the military calibers will remain available in great variety. That's one reason that .308 is such a good choice over the similar calibers based on its case. .308, in the form of the 7.62x51 NATO is still in use by the military and ain't going away. It's still used in light machine guns and mini guns. The coast guard qualifies with an M60 on our range from time to time and leaves me a lot of brass on the ground.
They sure tear the heck out of the 200 yard target boards that we have to repair/replace, but I do appreciate the brass.