Most dance photographers I know (and have observed) and I, predict the moment as we see it coming. Then we use a single click to capture it. Continual shooting is considered less than ideal. One wastes energy and film/memory. I have seen some green newspaper photographers use the fast click technique, but that is not the norm.
The challenge is not in just capturing the moment, but also having the correct exposure and frame/composition ready. Many photographers have a sense of the moment, but not the framing. The aesthetic sense of framing is commonly referred to as the "eye". So someone with a good "eye" will have interesting photos. I rarely crop a photo more than 10-30% of the area. In most cases what you see is the way the shot was taken.
Solos and duets are easy to shoot but corps work is a challenge, due to coordination of the dancers and size of formations.
Having said that, most photographers with digital cameras, can shoot close to 200 photos in a 20-30 min piece (depending on the style ad choreography). The final yield of "good" photos is smaller. I have noticed that in Ballet solos and duets, 20% of the photos are not usable. In corps work, 50-60% of the photos have to be thrown away. Artistic directors, and marketing eliminate more photos due to their stringent requirements.
My first experience of loving the work of a dance photographer was with Martha Swope, who created unforgettable b&w images of the early decades of the NYCB. (Not to mention that great photo of Balanchine watching Mourka, his cat, as he leaping into a truly prodigious tour en l'air.) (1)
I also admire the work done by Steven Caras, first at NYCB, and now for Miami City Ballet. Caras was a NYCB dancer whose photographic interests were encouraged by Balanchine. He has an uncanny sympathy for the way the dancer's body moves. I guess his most famous photo is not actually of a dance. It's Balanchine's last curtain call ("last bow") at the NY State Theater on closing night, 1982. (2)
Who are the dance photographer's you most admire? And what makes them special?
-- (1) Taper, Balanchine, p. 244.
-- (2) Tributes: Celebrating Fifty Years of New York City Ballet, pp. 112-113.