There's an amusing dialogue floating around about how simple SOAP is. As someone who bears some past responsibility for well used SOAP services (Google's APIs for search and AdWords) let me say now I'd never choose to use SOAP and WSDL again. I was wrong.
The promise of SOAP and WSDL was removing all the plumbing. When you look at SOAP client examples, they're two lines of code. "Generate proxy. RPC to proxy." And for toys, that actually works. But for serious things it doesn't. I don't have the space to explain all the problems right now (if you've seen my talks at O'Reilly conferences, you know), but they boil down to massive interoperability problems. Good lord, you can't even pass a number between languages reliably, much less arrays, or dates, or structures that can be null, or... It just doesn't work. Maybe with enough effort SOAP interop could eventually be made to work. It's not such a problem if you're writing both the client and the server. But if you're publishing a server for others to use? Forget it.
The deeper problem with SOAP is strong typing. WSDL accomplishes its magic via XML Schema and strongly typed messages. But strong typing is a bad choice for loosely coupled distributed systems. The moment you need to change anything, the type signature changes and all the clients that were built to your earlier protocol spec break. And I don't just mean major semantic changes break things, but cosmetic things like accepting a 64 bit int where you use used to only accept 32 bit ints, or making a parameter optional. SOAP, in practice, is incredibly brittle. If you're building a web service for the world to use, you need to make it flexible and loose and a bit sloppy. Strong typing is the wrong choice.
The REST / HTTP+POX services typically assume that the clients will be flexible and can make sense of messages, even if they change a bit. And in practice this seems to work pretty well. My favourite API to use is the Flickr API, and my favourite client for it is 48 lines of code. It supports 100+ Flickr API methods. How? Fast and loose. And it works great.
To be fair, SOAP can be forced to work. Using SOAP didn't really hurt adoption of the APIs I worked on. But it sure didn't help either. So what's the alternative? I'm not sure. Right now I'd probably go the HTTP+POX route while trying to name my resources well enough that the REST guys will invite me to their parties. But XML itself is such a disaster and AJAX is starting to show the cracks in HTTP (like, say, the lack of asynchrony).
Truly, none of this protocol fiddling matters. Just do something that works.
I no longer work for Google; these opinions are very much my own.