Normally, a WCF service will use SOAP, but if you build a REST service clients will be accessing your service with a different architectural style (calls, serialization like JSON, etc).
In terms of downside, you lose much of the work that has been done on SOAP header specifications (WS-* like WS-Security, WS-ReliableMessaging, WS-AtomicTransactions for example). Also, SOAP is transport neutral whereas REST presupposes HTTP.
Nice MSDN reference at:
http://msdn.microsoft.com/en-us/library/dd203052.aspx[
^]