Actually if you are just getting started and have at least VS.NET 2005, look into WCF. WCF will give you opportunity to have the best of both .asmx or remoting.
The Windows Communication Foundation (WCF) supports more protocols for transporting messages than the ASP.NET Web services support. ASP.NET Web services only support sending messages via the Hypertext Transfer Protocol (HTTP). The Windows Communication Foundation supports sending messages via HTTP, as well as the Transmission Control Protocol (TCP), named pipes, and Microsoft Message Queuing (MSMQ).
ASP.NET web services vs. WCF:
http://wcf.netfx3.com/content/TheFutureofASPNETWebServicesintheContextoftheWindowsCommunicationFoundation.aspx
If you want information specifically on ASP.NET .asmx web services look at the following:
http://msdn.microsoft.com/en-us/library/ms972326.aspx
If you want information specifically on remoting look at the following:
http://msdn.microsoft.com/en-us/library/ms973857.aspx
Performance .asmx vs Remoting:
http://msdn.microsoft.com/en-us/library/ms978411.aspx
Comparison .asmx vs remoting:
http://www.developer.com/net/net/article.php/11087_2201701_3