Server.Transfer() : client is shown as it is on the requesting page only, but the all the content is of the requested page. Data can be persist accros the pages using Context.Item collection, which is one of the best way to transfer data from one page to another keeping the page state alive.
Response.Dedirect() :client know the physical loation (page name and query string as well). Context.Items loses the persisitance when nevigate to destination page. In earlier versions of IIS, if we wanted to send a user to a new Web page, the only option we had was Response.Redirect. While this method does accomplish our goal, it has several important drawbacks. The biggest problem is that this method causes each page to be treated as a separate transaction. Besides making it difficult to maintain your transactional integrity, Response.Redirect introduces some additional headaches. First, it prevents good encapsulation of code. Second, you lose access to all of the properties in the Request object. Sure, there are workarounds, but they're difficult. Finally, Response.Redirect necessitates a round trip to the client, which, on high-volume sites, causes scalability problems.
As you might suspect, Server.Transfer fixes all of these problems. It does this by performing the transfer on the server without requiring a roundtrip to the client.