Pelt saving is an issue with a lot of cartridges, even smaller ones. The .308 is a good size round. Finding just the right bullet will be the problem, and it may take a lot of experimenting with a lot of coyotes on the ground before you reach some conclusions. Since you mentioned "predators," you no doubt are considering bobcats and fox too, which are thin-skinned animals, making it even more difficult to find a proper bullet, if indeed there is one. Even FMJs sometimes will expand and tear up more tissue than you might think. As well, from all the readings I have done, those bullets are not reliable killers, and the limited number of animals I have shot with FMJs bear that out. While I'm sure there are some guys who hunt predators with .308s, I imagine the numbers are few. In a nut shell, a .308 is not known to be a fur-friendly round.
Due to pelt saving, I purchased a .17 Remington this past summer and have taken two coyotes with it already, both were "drop-dead at the scene" with no exits. However, even the .17 Rem is sometimes destructive on light-skinned fox.