I just switched from a compound crossbow to a recurve, and I'll outline my reasons.
1) Noise: A compound crossbow is much noisier than a recurve (although all crossbows are noisier than their comparable verticle bows). I once had a moose that (my hunting buddy thinks) jumped the string on an older design recurve crossbow, so I'm very sensitive to this issue. My recollection is that the moose moved after the bolt would have arrived.
2) Complexity: With all those moving parts, it's just an accident waiting to happen. There are more places for twigs and pieces of grass to get in the way and throw the bow off. The Excalibur is about as simple as it can get.
3) String Changing: If something goes wrong with a string or cable on a compound Xbow, you usually have to take it to the proshop to be fixed or changed. I can change the string on my Excalibur in the field and in minutes.
I originally chose a compound bow, because the width of the bow was less than that of a recurve. This was because I was still able to walk well, and preferred still hunting to stump sitting (still do). I am no longer as mobile as I used to be, so this advantage is of less importance to me.