IMHO, web services are faster (in terms of implementation, not performance) and easier to implement than remoting. Web services are also sometimes used as the communication channel for remoting. Microsoft offers some good web casts on how to implement remoting with .Net (and some bad ones too) if you are really interested.
http://msdn.microsoft.com/events/
With Indigo in the Windows Communication Foundation on the horizon, you might want to skip the investment in Remoting. Using your current knowledge and expertise in Web Services, you should be able to continue your development in distributed applications or SOA (hopefully one of these two reasons is why you are using web services in the first place). When Indigo is available, there will be a large library of tutorials.
http://msdn.microsoft.com/webservices/indigo/default.aspx
