Started hunting with a 303, 40 some years ago. I think in those days, just about everybody's first rifle was an old 303 British. I used to use the Imperial 180 ST in those days. They worked on Badgers, Coyote, Whietail, Moose, Bear. Pretty much anything that moved, you could use 303 on.....and we did.
I don't really use the old 303 anymore, but I still have one, and a couple boxes of Winchester 180 gr Power Point, just in case I ever want to.