Server.Transfer 

Main difference between server.trasfer and response .redirect is that when we use server.trasfer our page processing transfers from one page to the other page without making a round-trip back to the client’s browser.  Server.Trasfer provides a faster response with a little less overhead on the server.  The clients url history list or current url Server does not update in case of Server.Transfer. 

Response.Redirect

It sends a http request to the browser then after browser resends that request to the webserver then webserver deliver response.When we use Response.Redirect it redirect the user’s browser to another page or site.  It also performs trip back to the client where the client’s browser is redirected to the new page.  The user’s browser history list is updated to reflect the new address.