The favorites (filters, transitions, motion effects, etc) that you keep in your Favorites Bin are part of FCP's preference file. You can make copies of your FCP preference to distribute on other computers IF each system is running the same version of FCP. However, I'm not sure which of the preference files that it is actually a part of.
Here's what I do to keep my favorites safe in the event of drive failure, system or software upgrade, fire, theft or other calamity:
1. Start a new FCP project named "Favorites."
2. Place a text generator or on the clip on the Timeline.
3. Cut the clip into as many pieces as you have favorite transitions.
4. Apply one favorite transition to each cut.
5. Apply favorite filters to one section of the clip. Or you can apply one or more filters to each clip section.
6. Apply each favorite motion to the clips.
7. Save the project and make a backup on removable media.
In the event that your system is stolen or perishes in a fire, or you lose a hard drive, upgrade your system or for whatever other reason, once you're back in business, load the Favorites project file from the removable media, then open the project and drag each filter, transition and motion favorite from the clips on the Timeline into your new Favorites Bin.
-DH