I have multiple options with 45, 50, 54, 58 and 62 caliber roundball guns. All work on whitetails.
Typically make my choice on what I carry based on hunting conditions. Have a 45 Cherokee, that is short and light, and can carry all day. Have successfully hunted with it a number of times, although early on I had a bad 45 RB performance experience, but we will just call that ‘shot placement’. Have a very thick spot (an overgrown clear cut) in the mountains and I only carry short barreled 58s when hunting there. Shoulder shots only for DRT, for if a deer takes only a few steps in the wrong direction recovery could be an all day project.
Distance wise, limit myself to 100 yards. All the hunting loads in my roundball guns are sighted for 100 yards (‘zeroed’ at maybe 75 to 90). All are over a foot low at 150 and three to five feet low at 200 yards...
What can you shoot well in your hunting conditions? Off hand, moving target that may not lineup broadside, wind, unknown distancees, trees/branches and such in the way, etc. Many ‘experts’ say shot placement. Not always easy to make happen.
45 or 50 will work. Picking one, I would advise going to the larrger caliber. As the saying goes, plan for the worst possible conditions, hope for the best.