Mozilla ports simplified private browsing app to Android
helpnetsecurity.com
helpnetsecurity.com
Even on iOS, it could do with some improvements, like responding to standard screen swipe gestures for back/forward, adding a share sheet to make it easier to export the current URL, etc. This may just be my experience alone, but it also feels slower and "heavier" (battery wise) than Safari.
In case "tabitis" sounds unfamiliar - http://www.urbandictionary.com/define.php?term=tabitis