There are benefits and downsides to using separate X screens for dual screen setups vs a “large desktop” which just means the computer thinks there is one desktop, with two monitors showing the same desktop.
Separate X screens means you have an entirely different screen on each monitor. This is useful to me because I can have two SETS of workspaces on each screen. My smaller monitor to the left has 3 workspaces, the large 30″ on the right has 6 screens. I keep my browser, chat, music on the left monitor, and it doesn’t move no matter how much I switch around on my main screen.
With a large desktop or TwinView, you would switch both screens by switching workspaces. So having that second screen doesn’t help THAT much if you already have a large main screen as you’d still need to switch around just to look on your second screen.
Anyways, FireFox complains that you an instance is already running if you try to run firefox on each screen. To get around the problem, start firefox with -P, which runs the profile selector.
Create a new profile and there you go, you have a new firefox instance running on your other screen.
From now on, just start firefox by running firefox -P.