Synergy isn't a remote desktop per se
, it's more like a software KVM. Using VNC, RDP or Teamviewer, you can view and control the desktop of a 'headless' computer (no mouse, keyboard or monitor). With Synergy, additional computers running side-by-side can be controlled from a 'master' as easily as if they were simply additional monitors.
My son demonstrated it this way: He has a Dell laptop with an Intel graphics chip that he uses for playing music, and a HP laptop with a decent AMD 3D graphics chip for projecting visuals via a projector as a 2nd monitor. With both laptops open and running next to each other, he can just slide the mouse over from the Dell screen, the pointer appears at the HP screen, and he's controlling it seamlessly; he never has to physically move to the other laptop keyboard and touchpad.
Can one set up Teamviewer so the 'remote' computer doesn't have to give permission to connect? That's one drawback I can see. With RDP or VNC, it can be set up to run on startup and 'listen' for a connection.
BTW - my preference is for TigerVNC -> http://tigervnc.org/