In essence:

Response.Redirect simply sends a message back to the browser, telling it to move to another page.

whereas

Server.Transfer conserves server resources. Instead of telling the browser to redirect, it simply changes the “focus” on the Web server and transfers the request. This means you don’t get as many HTTP requests coming through, which should ease the pressure on your Web server and make your application run faster.

Keep in mind though, because the “transfer” process can work on only those sites running on the server, you can’t use Server.Transfer to send the user to an external site. Only Response.Redirect can do that!!