Tough question to answer.
First off, I guess that you are talking about varmint hunting, and perhaps coyotes?
As for accuracy, it depends on the actual gun, load, etc. I have seen 25-06s shoot better than .22-250s, and vica versa.
600 yard shots? That's pretty darn far. I don't recommend such shots for anyone to take (at any animal that is). But if you are inclined to still shoot at that distance, the .25-06 will have more power at that distance than the .22-250.
Pelt damage? It depends more on the design of the bullet than anything else. A full metal jacket will generally pass right through, where as a soft point, or hollow-point, will create much more pelt damage.
Zachary