There is a difference:
Response.Cookies.Add()
will allow duplicate cookies to be set http://msdn.microsoft.com/en-us/library/system.web.httpcookiecollection.add.aspxResponse.Cookies.Set()
will make sure the cookie is unique by first checking to ensure the cookie doesn’t exist http://msdn.microsoft.com/en-us/library/system.web.httpcookiecollection.set.aspx
Duplicate cookies typically requires extra handling to determine which is the most recent. I’m not sure of a case when you would want duplicate cookies on the same site, maybe someone else can chime in with an example
Edit: In your case, you want to use set because you are updating.