I have used both for a very long time so I can give you a comparison...
Both share keyboard and mouse, and are reasonably easy to configure and run (though Multiplicity gets the nods over the long term).
I've found Multiplicity to be more reliable and better at recovering from a disconnected machine etc. - from either the client or server side.
Synergy is free and can be used on unlimited machines. Multiplicity is a bit pricey for something that only does one thing (though it does it well). You'll need Multiplicity Pro to work with more monitors/machines.
Both can copy and paste clipboard text/url, etc. But Multiplicity Pro adds file copying.
Synergy is no longer in active development and hasn't been updated in forever. Long standing bugs and feature requests seem to be dead. Multiplicity is still seemingly in active development with a recent bug fix just released.
I hope that helps. I used to use synergy for all my machines and now I use multiplicity pro for everything.