I think that main difference lies in the ability for the 308 to be made into a shorter, lighter, handier rifle without sacrificing almost any of its ballistics to start with.
You can go to 20", even 18", and lose hardly anything in the 308. With a stiff barrel, it maintains its inherent accuracy. And in my opinion and that of some others (for instance some African PHs), the slightly larger bore diameter leaves just enough of a larger wound channel upon entrance/exit even with stiff bullets that you get a more reliable blood trail when needed. I've not seen anything that a 30 caliber won't do as well or often "better" than a 27.
That said, it would be all about the "platform" for me, and how well if fits and feels in the field. 270 vs 308 is a tossup for most practical intents.
