Of the Pern books, Dragonsdawn is my favorite, but I also love both Moreta and Nerilka. Also, Dragonsong and Dragonsinger. I really like MHoP, but, as has been mentioned by others, found myself somewhat bothered by some continuity issues and the women's role that didn't fit with what was portrayed in other books. Loved Crystal Singer, first 3 books of the Freedom series. Absolute favorite is Nimisha's Ship. But enjoy everything she wrote alone, and most of the others.
I've not really read too much of Anne McCaffrey as i was always put off by the Fantasy element of the Pern series. what i did read, i did enjoy. I've read the Sassinak trilogy that she wrote with Elizabeth Moon and the Rowen/Damia series of books, which although i enjoyed them a lot, still thought that the series was perhaps longer than it should have been.
Choosing a favorite is always a struggle no matter what author or genre is in question. When I first discovered her writing in the early 70s she was a new author and I fell in love with Pern. At that point there were only 2 books in the set. Later when The White Dragon came out I had to buy it in hardbound because I could not wait. And while I still have a soft spot for the Pern novels I think I like some of her later books even more. Having somewhat of a musical background I think my favorites are a toss up between the Crystal Singer books and the Ship who Sang series of books.
Dragonsinger and Dragonsong, definitely. Though I enjoyed all the early ones, in different ways. I like the Ship Who Sang too. I used to go to France quite frequently in my teens and got into the habit of buying the French editions ... they must have been very popular in France at that time, because they were everywhere in the eighties. I still have several Pern novels in French kicking about the house. For when I want to be pretentious.