I'm using a keyboard shortcut to move any window, be it maximized or not, between monitors. This doesn't require Unity, but it does require Compiz (so you can also use it in Xfce if you've set it up to use Compiz for instance).
To do this, firstly, install CCSM and Compiz Plugins if they are not already installed:
sudo apt-get install compizconfig-settings-manager compiz-plugins
Then open CompizConfig Settings Manager, search for the "Put" plugin (it's under Window Management) and enable it. Then, click the plugin so we can change some of its settings.
On the "Bindings" tab, click on "Disabled" next to the "Put to Next Output" keyboard shortcut, check the "Enabled" box and then assign it a key combination that's not already in use. I've used Ctrl + Tab (click on "Grab key combination" to set a keyboard shortcut). Then click ok and you're done.
Now, focus a window and press the keyboard combination you've used above: the window should move to the other workspace. If you only have two monitors, this should be enough, as it moves any window from one monitor to the other. If you have more than 2 monitors, you can assign keyboard shortcuts for "Viewport Left" and "Viewport Right" and so on, under "Put to adjacent viewport".
More about this and other multi-monitor tweaks / fixes @ Ubuntu Multi-Monitor Tweaks (Full Screen Flash Fixes, Span Wallpaper Across Monitors, More)