The main exceptions to this are Flash cookies. These are shared between all browsers for a given user, since they're stored by the Flash plugin itself and independent of individual browsers' profile storage.
"Starting with Flash Player 10.1, Flash Player actively supports the browser's private browsing mode, managing data in local storage so that it is consistent with private browsing. So when a private browsing session ends, Flash Player will automatically clear any corresponding data in local storage."
Source: http://www.adobe.com/devnet/flashplayer/articles/privacy_mod...
Local storage here refers to "Flash cookies".