I shot my moose with a 168 TSX (2825 fps) out of a 30-06 at ~170 yards. My 308 win shoots the same bullet at 2725. I doubt the moose would have known the difference.
Around 45 grains of Varget is a good load for the 168 TSX or TTSX. I have recently switched to CFE-223 and am getting good accuracy around 47.5 5 grains and velocities in the 2785 range which gets your 308 awfully close to a 30-06.