REST is implementation-agnostic and much more transparent, and this makes it great for public APIs, especially for big websites like Flickr, Amazon or Digg that are using their APIs as marketing tools and really want people to consume their data. They don't want to be hand-holding 1000s of novice developers who are trying to debug their scripting language of choice's buggy SOAP library.
Versus SOAP and WSDL, which are better for internal applications, where you have drop-in libraries and known clueful people on both ends. (And you maybe don't have to care about things like Internet-scale load-balancing, HTTP caching etc.) Then you get APIs that are self-documented, preserve types etc. with zero work.