RESTful services are much simpler to consume than SOAP based (regular) services. The reason for this is that REST is based on normal HTTP requests which enables intent to be inferred from the type of request being made (GET = retrive, POST = write, DELETE = remove, etc...) and is completely stateless. On the other hand you could argue that it is less flexible as it does away with the concept of a message envelope that contains request context.
In my experience SOAP has been preferred for services within the enterprise and REST has been preferred for services that are exposed as public APIs.
With tools like WCF in the .NET framework it is very trivial to implement a service as REST or SOAP.
Some relevant reading:
- Amazon Web Services Blog: REST vs SOAP
- Dare Obasanjo writes often about REST
