I've shot a lot of elk with a 270 using 150gr Speer Hotcores. They've held up extremely well and are very lethal. 165's in a 30-06 should do as well or better.
I have very little experience with Winchesters. I reload everything and nobody around here sells their bullets.

“In a time of deceit telling the truth is a revolutionary act.”
― George Orwell

It's not over when you lose. It's over when you quit.