Qute, Firefox's old default theme (and Thunderbird's soon-to-be-retired default theme) doesn't have borders on its toolbars (at least in the latest Firefox version; see also the Qute FAQ). Winstripe, the new default theme, does. Personally, I prefer no-borders - it looks cleaner.
The Qute FAQ provides some CSS that can be added to your userChrome.css file to reinstate the borders. Based on this then, to remove Firefox and Thunderbird's toolbars' borders, add this to your userChrome.css file:
/* Remove toolbar borders */ toolbar {border-top: none !important; border-bottom: none !important}