I shot one moose and more than two dozen white tails with my Remington 788/30-06. It was an excellent, accurate rife. One of my best friend's brothers wanted the rifle and I sold it to him. He is still using it extensively, 20 years later.
I then bought a 30-06 BDL. Only shot one white tail with the BDL, plus a couple coyotes.
Since then I have got out of white tails, but still scare coyotes with a .243, BDL plus it is tricked out somewhat.
When I was younger in the province of Saskatchewan we used to shoot jack rabbits with a lead cast bullet (can't remember bullet weight or loads). The only rule was the rabbit had to be running.
I would recommend a 30-06 to anyone shooting big/ medium game in North America.