Both good rounds for whatever hunting long range accuracy.
I am old school. I load my 7mm Mauser up to pressures reserved for modern bolt action rifles. Accurate at long range. I load down my .30-06 rounds DOWN to preserve the mechanisms in my Garands and use the same for hunting as I dont need super long range here in the NE.
Excellent.
I have a bunch of rifles, and have killed 80-90% of the game I’ve shot in the last 30 years with a horribly abused Ruger in 7x57 Mauser with stout handloads, mostly 140 Barnes TTSX at about 2900 fps or a 160 partition at 2750 fps. I have shot exactly one animal twice, and this includes several up to elk/kudu size. This past fall I shot a 20 in inside spread whitetail behind the house at 368 yards running broadside with it. It’s just one of those when I pull the trigger I know something’s gonna die. As time goes by, about the only other rifle I hunt with is a custom one built on a commercial FN Mauser action in .338 WM. If I’m in a spot where there might be contact with a grizz, lion, etc, I hunt with the .338. For the really tough stuff, I have a .416 Rigby which is rarely used since my budget doesn’t afford those type of hunts on an annual basis! However, there would be no reason to not use a 7-08 to replace the 7x57, it just doesn’t have the history.