Define "stable"; -p
If you mean "time in the field", then for .NET the order will be SOAP (asmx), WCF, REST
Note that there is a big shift between data-oriented REST services (typical of ADO.NET data services) and WCF / asmx, which are work-oriented.
REST, , ; WCF/asmx ( ). , , , - ( WCF) ( ..).
WCF , -, .NET, WSE ( asmx WSE3). , WCF , asmx .