Both methods are used by many of the large players. It's a matter of preference. My preference is REST because it's simpler to use and understand.

SOAP:

• SOAP builds an XML protocol on top of HTTP or sometimes TCP/IP.
• SOAP describes functions, and types of data.
• SOAP is a successor of XML-RPC and is very similar, but describes a standard way to communicate.
• Several programming languages have native support for SOAP, you typically feed it a web service URL and you can call its web service functions without the need of specific code.
• Binary data that is sent must be encoded first into a format such as base64 encoded.
• Has several protocols and technologies relating to it: WSDL, XSDs, SOAP, WS-Addressing

Representational state transfer (REST):

• REST need not be over HTTP but most of my points below will have an HTTP bias.
• REST is very lightweight, it says wait a minute, we don't need all of this complexity that SOAP created.
• Typically uses normal HTTP methods instead of a big XML format describing everything. For example to obtain a resource you use HTTP GET, to put a resource on the server you use HTTP PUT. To delete a resource on the server you use HTTP DELETE.
• REST is a very simple in that it uses HTTP GET, POST and PUT methods to update resources on the server.
• REST typically is best used with Resource Oriented Architecture (ROA). In this mode of thinking everything is a resource, and you would operate on these resources.
• As long as your programming language has an HTTP library, and most do, you can consume a REST HTTP protocol very easily.
• Binary data or binary resources can simply be delivered upon their request.