I'll take the 7x57 any day. Especially if using heavy for caliber bullets. Regular factory loads are running the same as the 08 version now, for all practical purposes, and you can hand load the x57 version to near 280 velocities. Typically the x57's are in standard length actions, so the bullets don't have to be seated into your powder space. The x57 version was developed in 1892 and has taken every game animal on the planet in the hands of skilled marksmen worldwide. I know the stories Bell, and there are others, but I, personally, would not want to tackle any of the big 5 with any 7mm cartridge. I've got a 7x57 (or 7mm Mauser, 275 Rigby), and it is a grand cartridge. It's great for deer, sheep, goats, caribou and smallish moose. Factory loads are throttle down for the old rifles that were chambered for this cartridge, much like the 45/70. If you handload, it will handle nearly any hunting situation. Imagine that, something 111 years old that is every bit as good as a cartridge introduced in the last 20 years!!!
The advantages the 7-08 does have is that you don't really need to handload and it comes in short actioned rifles. That's both a blessing and a curse. If you don't handload, your rifle may not like factory loads. Being in a short action, it kinda limits the OAL which I don't like.