You are kind of mixing the matter up a little. Compound bows can be vertical (the one you have been referring to here) or can be purchased in a crossbow configuration. Rule of thumb here is pretty well anything with wheels / cams / cables & strings is considered a compound. Those bows without are generally referred to as straight / long bow or recurve. These too can come in either vertical or crossbow types.
There are many differences between a vertical bow and a crossbow. The two most obvious are the vertical bow gets the nod when stalking through the thick. The crossbow is more cumbersome when doing so. The largest difference is that the vertical bow must be drawn and anchored in the very near presence of game, whereas the crossbow is already locked & cocked.
Beyond that, they both shoot arrows, and as such are subject to the same limits regarding range and effectiveness. Most suggest a maximum distance of around 45 yards for both. Good general rule of thumb is shoot out to increasing distances. At the range your groupings open up to around four inches, you have reached your max. Practice, and high end equipment can extend this for many.
I found the vertical bow a little trickier to master (when I could still draw one that is). For those familiar with shooting a rifle, the crossbow is generally a little more familiar, and thus easier to come to some sense of proficiency with. Both however do require a good amount of practice in order to become proficient enough to hunt with. That said, today's modern equipment is downright amazing. Most bows of either type are quite User Friendly in comparison to the stuff we had 40 years ago!
Boils down to personal preference for most. I'd suggest trying out a few of either type and letting the bows tell you which you prefer. Anyone who lives or wanders close to Port on the Island are free to give me a shout in that regard. If I have a little free time, I certainly do not mind showing someone the recurve crossbow ropes as it were...
Good Luck with your selection!
Cheers,
Nog