I have the overall feeling that most people don’t realize that parser combinators are nothing more that disguized recursive descent parsers. Personally I love both.
They're not, though. They're a formal language for talking about all kinds of parsers. You can implement them as recursive descent if you want. You can also compile them into formal FSAs if you want.
Parser combinators are a quite general technique which has been applied to PEG parsing, Earley parsing, and many other specific algorithms. Recursive descent is common because it is easy to implement and allows the resulting combinators to form a Monad.