The two protocols have very different uses in the real world.
SOAP(using WSDL) is a heavy-weight XML standard that is centered around document passing. The advantage with this is that your requests and responses can be very well structured, and can even use a DTD. The downside is it is XML, and is very verbose. However, this is good if two parties need to have a strict contract(say for inter-bank communication). SOAP also lets you layer things like WS-Security on your documents. SOAP is generally transport-agnostic, meaning you don’t necessarily need to use HTTP.
REST is very lightweight, and relies upon the HTTP standard to do it’s work. It is great to get a useful web service up and running quickly. If you don’t need a strict
API definition, this is the way to go. Most web services fall into this category. You can version your API so that updates to the API do not break it for people using old versions(as long as they specify a version). REST essentially requires HTTP, and is format-agnostic(meaning you can use XML, JSON, HTML, whatever).
Generally I use REST, because I don’t need fancy WS-* features. SOAP is good though if you want computers to understand your webservice using a WSDL. REST specifications are generally human-readable only.