Whichever Suits You Best
The most straightforward answer to this question is which will you prefer. For many beginners, Rifle Hunting is the way to go because it's a lot more of a clean process. It bores a hole, and then you just have to walk down your kill, and that's it.
But for many avid hunters, bow hunting is the preferred version. Not only are there more hunting days permitted on average, per state, which makes it advantageous for those who enjoy hunting multiple times a season; But it also gives a feel of authenticity to the kill if you are more interested in the classic way of hunting.
But which one will suit you best?
Bow Hunting is Superior
Bow Hunting has a lot more versatility than rifle hunting. There are multiple things you can do without switching up your bowhunting style. For example, you have compound vs. bow fishing bows. Releases are being much more commonplace, which makes them more similar to a rifle in case you need assistance with draw strength or aim.
Additionally, in terms of practice, it's much easier for you to maintain your skills on the range with bows and arrows. Typically upkeep cost on bows is much lower than that of rifles though it generally is the same for the cost of entry.
So if you're looking for a low-cost way to enter into hunting, this one has arguably better variability in the long run.
Rifle Hunting is SuperiorRifle Hunting is much easier to use.
Not only are rifles much less physically demanding than bow and arrow, but they are also much more effective at ensuring the kill and reducing the struggle.
So if you are having issues with dropping your prey or you want to ensure the kill more succinctly, then rifles will be the more advantageous decision.
With that comes stricter licensing, registration, etc. But if hunting is your game, these will be minor annoyances as opposed to great hurdles.