The Java EE 6 Tutorial

Deciding Which Type of Web Service to Use

Basically, you would want to use RESTful web services for integration over the web and use big web services in enterprise application integration scenarios that have advanced quality of service (QoS) requirements.

Note –

For an article that provides more in-depth analysis of this issue, see “RESTful Web Services vs. “Big” Web Services: Making the Right Architectural Decision,” by Cesare Pautasso, Olaf Zimmermann, and Frank Leymann from WWW '08: Proceedings of the 17th International Conference on the World Wide Web (2008), pp. 805–814.