We have a URLRewriting module that is using a Response.Redirect in the BeginRequest event method to change the destination page.
The following questions cover the differences between redirect and transfer but not within an HTTP Module;
EDIT: HttpContext.RewritePath is also used in the module so it seems we have three techniques to move the initial Request from the original path; Redirect, Transfer, RewritePath which respectively; go back to browser, back to start of HTTP pipeline and continue processing on new path.
Here's the best explanation of Redirect vs Transfer vs RewritePath; http://www.developerfusion.com/article/4643/implementing-http-handlers-in-aspnet/4/
To summarise; Redirect requires roundtrip to browser, Transfer ensures the original Request object remains not the new request but has problems with Post-backs, Rewrite loses the orginal Request object but is the best for performance.