What is the difference between the following:
When should I decide to use which?
Server.Transfer tells ASP.NET to redirect processing to another page within the same application. This happens completely server side. This is more "efficient" as it happens on the server side but there are some limitations with this method. The link below describes some of these.
Response.Redirect actually sends a HTTP 302 status code back to client in the response with a different location. The client is then responsible for following the new location. There is another round trip happening here.
PostBackUrl is not a "transfer method" but rather an property that tells the browser which URL to post the form to. By default the form will post back to itself on the server.
Here's a good link: http://haacked.com/archive/2004/10/06/responseredirectverseservertransfer.aspx