Even if both could be used as the sam, for mexican people, "Apetecer" is related to something you would like (It is so common expresing in the desire of eat something : "¿Apeteces este chocolate?"), and "desear" is a deeper feeling.
The funny thing is that mexican people do not use a lot the word "apetecer" (it sounds old or so polite), and we use a lot the word "desear"