The 6.5 x 55 is simply one of the world's greatest rifle cartridges, for both hunting and serious, world-class target shooting.
It will do it all on game the size of moose or elk. Just use a premium 140-grain bullet pushed by a stout charge of H4831 (or similar powder). It's hard to beat 47-48 grains of H4831 or Reloder 22 with a 140-grain bullet in a good bolt rifle. Probably an even better choice would be the new 130-grain Barnes TripleShock pushed by the same powder. I would expect that bullet to go right through an elk or moose.
Though I haven't tried it yet, I would not be surprised if someone announced that the 130-grain Triple Shock pushed by Vihtavuori N560 makes the greatest all-around hunting load in the 6.5 x 55. That powder is really impressing me these days, burning in the ballpark of Reloder 22 but giving much higher velocities at comparable pressures. And the Barnes Triple Shock makes no apologies to anyone, as far as accuracy and killing power go.