Here in Ohio we allow both rifle/shotgun and bow hunting. I think part of it comes down to the power in each of the two items. We have 40 pound minimum draw weights on the bows here for hunting. So these bows should be able to pack a bit more of a punch when they hit. Couple that with a larger cutting surface, and the game should go down after a while.
Now, this after a while bit is probably where compassionate lawmakers disagree. Hitting a whitetail with a bow has many different recommended times to let the deer scamper off and bleed out. I think the minimum recommended time to go chasing after it is approximately an hour. In that time, the deer may be bedded down and bleeding out. Some people may cringe at that thought.
Now let us transfer over to the gun part of things. Guns pack a good bit of power in them. I have seen a well place shot drop a whitetail in its tracks. From initial stun to death in mere seconds.
I am not saying that 100% of the time gun will beat out bow though. It is all in the hands of the hunter. We assume everyone will be ethical about it. Let's not try a bow shot of 100 yards or let's not try 200 yards on a shotgun. Both can be made, but not by all hunters. I think lawmakers take that into account somewhat. I would assume the terrain would also play into it more as well for safety reasons. For example, we're only allowed straight-walled cartridges in Ohio for hunting. We are not as isolated though and a 30-06 round might end up going a bit too far for safety reasons.
Lastly, another reason to only allow bow/gun or gun could be related to hunter safety. I don't particularly mean hunter shooting hunter as anyone donning the blaze orange knows that is a distinct possibility. I am meaning when hunting predatory game like bears. I have seen YouTubers do it, but I would not want to try to take a bear with my bow. I can guarantee that if I shot a bear with my bow and angered it, I would not have enough time to get another arrow and draw before its upon me with all its fury. Of course, there are others different than I, and they would gladly accept that challenge.
These are just reasons off the top of my head why one might allow only certain items for hunting. The main thing to remember is that laws apply to everyone, regardless of skill. So, you really need to take that into account like the lawmakers hopefully did. You might get lucky and be able to find some write up by the legislative or judicial bodies as to their justification in certain laws or decrees.