You are not missing much. Here's my expereince. It may help (or may not?!?). I started archery hunting in 1962, and have been an avid archery hunter since. As I have aged, and as the result of injuries, over these past 5 decased or so I have transitioned from recurve to compound to cross bow.
The cross bow's chief advantage for me is not having to draw and hold. That is about it as far as I am concerned. And not to be minimized. I have been detected I do not know how many times as I tried to draw and have woatched as the deer bounded off. Plus anyone that has hunted with a stick, recurve or compound has been through the scenario of having drawn at an opportune moment only to have the game hold up ... sometimes for so long a period of time that letting off was required. The other advantage of a cross bow (somewhat) is that "becoming an accurate shooter" training time is less. Not to mean at all that practice is not necessary. The "scopes" that are out there for cross bows are certainly a great help in ending up with small groups. And the similarity of the ceross bow and a rifle as far as stock and trigger certainly are an advantage as far as becoming familiar with the "how to".
As far as effective distance, I have not found any advantage. I have target shot at 60 yards and am consistently well inside a 6" circle. But that is under ideal circumstances and of course the target cannot "jump the string"! In the field, I stay wth about the same self imposed limit of 40 yards +/-. The one bad placement that I made was a shot at a nice buck that was ranged at 42 yards. He was able to wheel away from me but the pass through path turned out to be lethal. Had he wheeled toward me, no telling !?!
I did find the cross-bow to be a whole different animal in several other ways. What I struggled with the most were: the requirement of a "horizontal" physical clearance requirement for the limbs, the increase in the noise of the cross bow release, and the difficulty of managing a second shot. I have wanted to make a second shot only once and was able to pull it off .... but that was because I was extremely well hidden and was able to c*ck the bow very quietly.
If I had my druthers I'd have stayed with my compound, but I cannot. So I use the cross bow and am thankful to be able to do so.