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.
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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.
Top Tip: Don't confuse Server.Transfer with Server.Execute, which executes the page and returns the results. It was useful in the past, but, with ASP.NET, it's been replaced with fresher methods of development. Ignore it.

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A common misconception is the difference between Server.Transfer and Response.Redirect in ASP.NET applications. Redirect and Transfer both cause a new page to be processed, but the interaction between the client (web browser) and server (ASP.NET) is different in each situation.
Redirect: A redirect is just a suggestion – it’s like saying to the client “Hey, you might want to look at this”. All you tell the client is the new URL to look at, and if they comply, they do a second request for the new URL.
If you want to pass state from the source page to the new page, you have to pass it either on the URL (such as a database key, or message string), or you can store it in the Session object (caveat: there may be more than one browser window, and they’ll all use the same session object).
e.g. Redirect to the new.aspx page, passing an ID on the query string. "true" stops processing the current page: