you can use any combination of quicktime 7, vlc and mplayer to play 2 separate videos independently on a dual screen setup.
further you can set one move playing fullscreen in quicktime on one screen while playing youtube fullscreen on the other. the only restriction is that youtube requires its window to remain the active window to remain in fullscreen. this is a platform independent problem.
if both videos need to be youtube videos:
1) get click2flash for safari
2) navigate to your first youtube video
3) select "watch fullscreen in quicktime" from the click2flash menu. (obviously make sure quicktime is configured to use the other screen)
4) navigate to second youtube video
5) select "load flash" from click2flash menu.
6) hit fullscreen youtube control