What are the advantages of the Burley hitch design?
The spring hitches seem to be a cheap/simple way to allow the flexibility needed to both bend and twist when the tow bike corners, but they have an annoying side effect. In my experience when accelerating hard on a bike with a loaded trailer connected by a spring hitch you can feel the spring stretch with each hard pedal pulse then snap back in to place with a bump.

So Burley might have this new design to eliminate this bouncing effect. 

Chariot/Thule hitches don't use a spring, they use both a ball joint and a flex polymer arm which makes them feel a lot better.  Their ball joint rotates easily for normal cornering and leaning, and the stiff polymer doesn't normally flex or stretch noticeably but can bend in extreme situations as a kind of 'fuse' to save the aluminium arm from breaking and/or the bike frame.