In my experience on Windows, IE was still faster than Firebird. Firebird doesn't load the page until it is all downloaded, so the page snaps to the screen fully rendered - whereas IE will render it as it gets the data, so it fills in and it gives the illusion of being slower.
Also, IE is C/C++ and Mozilla is largely Java. Mozilla will freeze up easily and also take a ton of memory.
IE allows you to spawn multiple instances of the process (not just of the windows) which means that if you are having issues with one of the processes, then you can kill it and it will fix that issue - but you don't lose all of the other windows.
Java based stuff doesn't always work that way due to memory spaces - but in Windows it is feasible still to spawn multiple Firebirds, but you would then get a huge memory hit.
In the end, I wasn't all that impressed with it.
There are browsers based on the KHTML browser and that is actually faster than the Mozilla stuff for sure.
In the end, like you say, it probably matters what you have going on in there.