Dijkgraaf - 9:03 pm on Jul 4, 2012 (gmt 0)

Chrome does seem to share the cookie with other incognito tabs (log into a site on one, and you are logged in on another one also), but not with the browser window that is not incognito. So you could have two Chrome instances running, one incognito and one not and log in with the different sets of credentials.

Firefox actually closes down and saves the tabs of the non-private session and won't open up a non-private one until you shut the private one, again any of the private sessions look like they can access the cookie (logging in with one tab means you are logged in on the other ones, even in a new window).