The JLC is surely a work of art, craft and finishing, but its wearability seems very limited. The JLC is quite a dressy piece, possibly only apropos worn under a cuff and with more formal attire. The Breguet can do double-duty...dressy enough to wear in most situations while also being industrial enough to wear more casually.
I also like the overall look of the Breguet more, it being more masculine as compared to the JLC's much more feminine styling.
Lastly, the JLC looks similar to many other skeleton pieces, whereas the Breguet is identifiable as uniquely Breguet -- there's really nothing else like the Tradition out there. Breguet blazed a trail with this line of watches.
So for me, the contest isn't close. I'd take the Breguet every time.
Cheers,
John