I depends what your goals are honestly. I'm not trying to muddy the waters. If you want to spend lots of time in the woods, kill a doe for the freezer, and that's all your interested in - I'd take up bow hunting. It's the most pleasant, enjoyable, laid back type hunting. BUT, bow hunting is a huge committment of time. If you choose a compound bow - you have to spend hours and hours of practice and keeping yourself sharp. A crossbow is much less of a time committment, but still more than a muzzleloader or rifle.
If you are interested in killing a mature buck and you are into diehard whitetail action and you can only afford one weapon - I'd recommend a muzzleloader and use during rifle season as well.
If you only have Thanksgiving week and Christmas week to hunt, as many who work do - then I'd probably just opt for a rifle.
It really depends on what your goals and desires are. Muzzleloader and rifle are much less of committment. Sight them in. Practice a little and you are ready to go. Bowhunting is much more equipment-centric. There are strings and cables to replace, practice, adjustments, ranging distances, keeping broadheads sharp, etc.
All that said, and all things being equal - if you could only afford one weapon, with today's modern muzzleloaders - I'd choose a muzzleloader. I just want those extra two weeks during prime time and (hunting in East TN) the muzzleloader has very little downside to me if I use it instead of my rifle during rifle season. I can't recall ever shooting a deer a second time during rifle season - except to finish off a deer quickly that was going to die anyway.
