Twitter favorites are pretty much hidden and have almost zero social component. On twitter, favorites are tantamount to me printing out my browser's bookmarks list and posting it on my front door.
FF likes communicates that you are interested in an item to the FF system, the poster, and other people who come across it. Activity on things you like reset their freshness (for you) so you don't need to go hunting for things that have had activity. The poster can immediately see if people are tracking activity on something, and get a feel for other's responses to their entries. And as for other people seeing who has liked what, I've found other interesting people to follow more closely based on their name showing up in the like list. When start seeing someone's name pop up often, it's a way to learn what they are interested in (other than from their own posts, of course).
Facebook has a history to incorporating other sites' features. When Twitter got big, they created added "status". We should all do that with our companies.
Facebook had a status feature before Twitter was founded. They made it more prominent after Twitter became popular but I think that was just a coincidence.
Not just facebook... every other company in silicon valley is doing that. Even google's adwords was first invented by overture. Latest eg. Palm Pre (and 15 other smartphones) incorporating iPhone UI elements.
