Ballistically, they are very close. For hunting, it would be a toss up IMO.
However, when you say "long range setup" I'm going to assume you mean target, and from that respect I would give the nod to the .06.
Target bullet selection, especially Match and VLD types, are very limited in the .277 caliber. Not much to work with there, and I don't need to tell you that the selection of .308 bullets is mind boggling. Me, I would go with the .06 because of bullet selection/availability.