I am of the opinion that your chosen weapon will get the job done. Carefull target selection and good shot placement are critical. If you are walk hunting and jump a great big 'ol boy in the bushes,(or foolishly try to track one in the dark) the .308 ain't the best choice, (35 Rem or 45-70 Govt spring to mind) but a well placed double tap, with the .308 will work.
I recently built a FN-FAL specifically to kill hogs.( predator control) we typically shoot from a buggy and take full advantage of NV gear and IR filtered spotlights.
The barrel is cut to 17 inches with a brake installed. This weapon is heavy, short and fast handling, almost totally recoil free and swings very much like a shotgun, on running hog's. When we jump a sounder, the goal is to kill 'em all, DRT is preferred, but not always possible. I use 150 Gr. HPBT at 2800 FPS and get very few run off's.
Again, this isn't your kind of shooting, but it shows what the .308 is capable of. Paul