While hunting the advantage is less movement to get on target and take the shot, thats about it. I'm not sure where ppl got the idea that they have longer ranges, but its a myth.
The real advantage of x-bows is getting more ppl into the sport. I know, I live in an area with a 2 week gun hunt, that wasn't enough for me so I bought a x-bow simply to take advantage of the longer season. Guess what, I never took a deer with it and hated carrying the monstrous thing around, so I bought and learned to use a compound, now my x-bow gets a workout bringing others into the sport. A few friends have tried my x-bow and have since bought compounds.
As for disadvantages; they are heavy, VERY loud, and I have a stand that I can't use it from because the limbs would hit branches as they come forward on the power stroke because it is horizontal instead of vertical.
I have both but use my compound every chance I get, even now when the season is winding down and I haven't taken a buck yet. I'm pretty sure most x-bow antis would change their tune if they hunted with one for a day.