Server.Transfer transfers the currnet context of the page to
the next page and also avoids double roundtrips. Whereas
Response.Redirect could only pass querystring and also
requires roundtrip.

Hai..,
Server.Transfer:
In Server.Transfer Page their is no round trim between 
client and server.if u requested a  page to server it will 
directly taken from the server itself

Response.Redirect:
-Round Trim between client and server:
- if u request a page
Example:
client-->server-->client

Server Transfer simply tranfer execution to another page . 
This doesnt require any information to be sent to the 
browser that is it all occors on the server without the 
users knowledge, doesnt update the client's URL history 
list or current url
Response Redirect method sends HTTP information to the 
browser instructing it to go to another page perform round 
trip back to the client when the client's browser is 
redirected to the new page.The user's browser history list 
is updated to reflect the new address.

Response.Redirect simply sends a message down to the 
browser, telling it to move to another page. So, you may 
run code like: 

Response.Redirect("WebForm2.aspx")
or

Response.Redirect("http://www.karlmoore.com/")
to send the user to another page.

Server.Transfer is similar in that it sends the user to 
another page with a statement such as Server.Transfer
("WebForm2.aspx"). However, the statement has a number of 
distinct advantages and disadvantages.

Firstly, transferring to another page using 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 
quite as many HTTP requests coming through, which therefore 
eases the pressure on your Web server and makes your 
applications run faster.

But watch out: 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.

Secondly, Server.Transfer maintains the original URL in the 
browser. This can really help streamline data entry 
techniques, although it may make for confusion when 
debugging.

That's not all: The Server.Transfer method also has a 
second parameter—"preserveForm". If you set this to True, 
using a statement such as Server.Transfer("WebForm2.aspx", 
True), the existing query string and any form variables 
will still be available to the page you are transferring to.

For example, if your WebForm1.aspx has a TextBox control 
called TextBox1 and you transferred to WebForm2.aspx with 
the preserveForm parameter set to True, you'd be able to 
retrieve the value of the original page TextBox control by 
referencing Request.Form("TextBox1").

This technique is great for wizard-style input forms split 
over multiple pages. But there's another thing you'll want 
to watch out for when using the preserveForm parameter. 
ASP.NET has a bug whereby, in certain situations, an error 
will occur when attempting to transfer the form and query 
string values. You'll find this documented at 
http://support.microsoft.com/default.aspx?id=kb;en-
us;Q316920.

The unofficial solution is to set the enableViewStateMac 
property to True on the page you'll be transferring to, 
then set it back to False. This records that you want a 
definitive False value for this property and resolves the 
bug.

So, in brief: Response.Redirect simply tells the browser to 
visit another page. Server.Transfer helps reduce server 
requests, keeps the URL the same and, with a little bug-
bashing, allows you to transfer the query string and form 
variables.