However, there are two issues that drive people crazy:
1) When you go enable full screen mode for an app, the app fills one display and all other displays are blanked with a gray linnen texture. That's may be useful if you are watching a movie and don't want other displays to annoy you, but it's really annoying if you just want eg. Mail full screen on a secondary monitor.
2) Mac OS Lion also added a feature named "Spaces" (I think this is called virtual desktops or so on other platforms). The problem is that when you switch between spaces, both screens switch simultaneously. Now let's assume you use your secondary monitor to show an IM client, or to show some live error log, or similar, it's really annoying if that disappears when you switch between spaces on your main display.
So OS X 10.9 finally makes two features introduced in 10.7 (Full screen mode, spaces) usable for people with multiple monitors.
Can you explain how is this fixed? Are the spaces on each monitor independent or is there a method to "always show" certain windows? Because I really hate the former method.
The problem was always how those two features interact with multiple monitors, nothing more. And, honestly, I think the fullscreen functionality was never intended to be used on larger screens. That’s for the MacBook Air, not anything larger.
But, yeah, Apple changes how the fullscreen functionality and Spaces interact with multiple monitors. (And personally I cannot understand why anyone would use apps in fullscreen mode at all. It just such a waste of space.)
Anyway, for an example of how fullscreen makes sense I suggest you look at video or audio editing software. You just need all the space you can get there.
Now Exposé.. that's another story...
Also, you could give apps the full screen to work with since forever in OS X. You do not need a special mode for that. Apple’s fullscreen mode is most definitely not in any way equal to Windows’ maximize function. I think that’s what many people fail to notice.
In Gnome (at least when I left it, but I don't think it has changed) and previously in OS X, switching to a new virtual space will update both monitors. With this update you choose virtual space independently for each monitor, and let one stay at — say — the logs window, while you change the space on the other monitor.