Comparing SOAP to REST for building web services is a bit like comparing apples with pears: SOAP is a protocol, REST is a pattern, and you could, if you felt so inclined, write RESTful services using SOAP. However, when people ask this question, they usually mean: SOAP (as in WSDL, perhaps RPC style, WS-* standards), as opposed to REST (as in JSON/XML over HTTP)
Assuming you mean this, below are some pros and cons for each, but note this: REST is increasingly becoming the de-facto standard across the web, being used by the big public API providers in preference to SOAP. I reckon it's just a matter of time before this question will just go away.