Yep, as UVvis says, the L5 head will fit/run on your C3... with the benefit of somewhat enhanced runtime. I haven't had a chance to test my L5's head on my old C3 yet, so I'll defer to others here.
As to getting the new (gen-2) KL3 head -- instead of an L5 or just the KL5 head -- that depends on what role you want it for.
I recently added my new L5 to our "night walks" light arsenal. As a result, my old "throw" lights are gathering dust. Oh, I still carry an Inova XO3, or Pelican M6 incan, or the new Pelican 3-watt LED -- strictly as a coat-pocket back-up.
I've just found that the L5's beautifully balanced beam (great flood, acceptable mid-range throw) is perfect for illuminating the woodsy shadows 25-40 yards out in our suburban neighborhood... without constantly swinging a narrow-beamed throw light all over the place to see what's out there. It all depends on your needs.
It's true that the L5 ain't a great runtime light -- it does chew through batteries about twice as fast as the new KL3 thrower with its flatter output.
No big deal. I figure that L5 will cost me about $15 more in batteries per year than something like the KL3 thrower. However, the L5's more versatile illumination benefits are easily worth that in terms of safety and visibility. YMMV.
Beyond that, the L5's flood probably makes a better Indoors light for lighting up a room in some home-intruder/self-defense shooting scenario. It's really kinda like an L4 on steroids in that respect.
Maybe your best solution would be to get BOTH the KL3 (throw) and the KL5 (flood) heads for your C3! Then, if you find the C3 unwieldy with either head combo, you could always buy an L5 or C2 body later and screw the LED head on it.