I don't currently have a 7x57 but I really should get one. I have much love for all three and wouldn't hesitate to use any of them on plains game or any North American game. I shot a bison last year with my 9.3 an dmy '06 has killed deer, caribou and moose. In fact, I stored all of my other rifles in favour of the 9.3 and 30-06 when I was posted to the far north this summer. Faced with moose, caribou, muskox, grizzly and polar bear I decided that these two covered my bases nicely, though a case could have been made for several of the others. I tend to be a "bigger is better" kinda guy so I would tend towards the 9.3 for heavier game and the 30-06 for everythign else, btu the 7x57 isn't too far behind at all. My lack of experience is the only thing that prejudices me against the 7x57 for use on heavier game. I'll steal the Old Man's rifle and shoot a few things to clear myself up.

"This duty fell upon me and was the worst job I ever had in my life.
I have known men I would rather shoot than the worst of dogs."

Frank Wild
Second in Command
Endurance 1914-1916