Although this problem has come about with Firefox 14.0, I'm reporting it as a TB bug for reasons that will become clear as you read on. I've also reported it as a bug to Mozilla.
I have two machines which both run Firefox (non-portable version) as default browser. Up to and including Firefox 13, if I clicked on a URL in an email in Thunderbird (portable) with Firefox already running on the machine, a new tab would open showing that URL, as expected.
Since the upgrade to Firefox 14, that no longer happens. Instead TB tries to open a new instance of Firefox and fails with a warning that it's already running.
I have tested this with URLs in other programmes (such as Pidgin portable) and everything still works as expected, so this seems to be specific to the way TB passes the URL.
Others have reported (in connection with the bug report I filed) that if the default browser is other than Mozilla, all works as expected.
I don't have a Thunderbird non-portable installation so I haven't been able to check to see if the issue is specific to the portable version.