Movie Edit Pro MX has a realy nice feature that I have been utilizing frequesntly. You no longer need to open the other project to copy clips to your current project.
Just locate the project in the directory where it is saved under the import tab in MEP.
Then right click the project and choose "Display Project Content". Click on the folder and you will see all the clips in the project you want to copy from. Just drag them to the timeline and you will get the clip with allthe effects that were applied..
This is the best method when copying clips. If you want to copy a section of the timeline, then the method John gave will work best,