IMHO, and mostly from what I have read (actually all from what I have read, having never shot a Buffalo), I would use the .308 with the best bullets I could find. Remember, these things are bigger than Elk, and while a .308 is legal for Elk, many a new cartridge from .338 to .375 in bore diameter has been developed for shooting Elk. If I had such an opportunity, it would be my excuse to build up a .338-06, a .338 Federal or a .35 Whelen
All kidding aside, you will be operating at the upper end of that cartridge's effectiveness, so use the very best bullets you can.