I have a good friend that killed his first 8-10 bulls with a 25-06 because it's all he had. It's certainly not ideal . . . he now shoots a 300 RUM and Berger 210's. Bang . . . Flop.
I'd also vote for the .270, provided that it's a shooter. If you can't trust its accuracy, it's a spear.
I shot a 30-06 for years when I was living on the East coast and it killed everything in my path. When I moved out West, it was inadequate as it would shoot 3"-4" groups at best with hand loads.
back to the point, the advice given previously is good.