In Scandinavia they use the 6.5 for moose routinely. Moose have a reputation for being stupid tough animals.
The 6.5 has the advantage of less recoil due to a lesser initial velocity and lighter bullets.
The -06 has the advantage of more power and heavier bullets....however:
To equal a 6.5 140 gr. spitzer in B.C a -06 needs a bullet of over 180 gr. assuming same style from same maker. The 6.5 will have a slightly better S.D.
In a 6.5 140 gr. vs. -06 180 gr. top velocity contest, the -06 bests the 6.5 by about 100 fps. according to my Hornady and Speer manuals.
The -06 can make a bigger hole since you have a bigger bullet to start with.
If recoil is going to be a deciding factor, the 6.5 is probably your better bet.
If total available power is the factor, the -06 wins.
If component or loaded cartridge availability is most important....see what's more locally available.
Edit: You can load the -06 down...the question is how well will your particular rifle shoot with starting loads under 130-150 gr. bullets.