I'm not sure about that.. but firefox does give you lots of control over the cookies. Boiled down, IE basically has 3 modes, allow all cookies, disallow all cookies, or prompt for all cookies. It of course has an exception list to the first two options.
Firefox has those 3 options and a new one that may cause funny reactions on some sites. The 4 firefox option basically amounts to fooling the website into thinking that it is accepting all cookies, while in fact it is only allowing those cookies per session. In other words when I log off, the cookies are gone even though the website thinks they were set permanently.
That is extremely simplified, and I am not sure of the exact reaction of that setting across multiple tabs. Extremely new versions of firefox have made even less information passable from one tab to another due to a recent security problem resulting from inter tab communication. This may in fact be the cause. I usually run the nightly builds, and my Firefox is usually no more than a week old. I'm sure the guys that run the site can test it though.