Changes are coming to way Firefox handles Private Browsing with Firefox 20 due out in early April 2013. In private browsing mode your browsing history is not saved and your existing cookies do not carry over into session, nor will any cookies from the private browsing session carry back to your main session. Currently in Firefox when you enable Private Browsing, your current session is saved and Firefox ‘restarts’ in private browsing mode. When you are done and select the Stop Private Browsing option, Firefox ends the sessions and ‘restarts’ back to where you left off prior, reloading your tabs and windows as they were prior to entering into Private Browsing mode. In Firefox 20, much like with Chrome’s “incognito window” Firefox will have the option to open links in a Private Browsing Window along side your current browsing session.
The new Per-window Private Browsing can be previewed in the current nightly builds. Again, this should be live with Firefox 20 in April 2013.
Source: Future of Firefox