Stuart Parmenter, aka Pavlov, has written an article on the improvements of Firefox 3 memory management. Firefox 3 uses a number of nice techniques to reduce the memory usage over time and it looks very promising. My experience with earlier versions of Firefox is that they over time consumes more memory and releases less than Internet Explorer. Pavlov shows with a number of graphs that Firefox 3 beta 4 outruns Internet Explorer 7 and previous versions of Firefox in good memory management.
I did a small test on my own to compare beta 1 of Internet Explorer 8 and beta 4 of Firefox and the results was not that surprising. Take this comparison with a pinch of salt since it not that scientific...
As you can see Firefox (3 beta 4 and 2) outperformed Internet Explorer 8 beta 1 and uses about 50 Mb of memory, in the end, on my machine while IE8 uses twice the amount. What you can't see in this diagram is that FF3b4 did use momentarily more memory, but I did not write these number down instead I wrote them down after the memory usage had stabilized after a few seconds.
Firefox 3 is really looking good and is now contending for the number one browser for me (the lack of creating ActiveX objects, which are used in SharePoint to open/edit documents, are now the only show stopper).