I would personally take the ZX6R. I'm actually surprised at how little weight difference there is between the two, but either one should be fast enough for any purpose, both will have very race oriented ergonomics that will make them terrible for long distance trips so if you're already committed to that there's nothing to be gained or lost there. The ZX6R has a noticeably shorter wheelbase and should be more nimble at low speeds, e.g. commuting.
But at a $5896 price difference between the two, you could use the change left over from buying the Kawasaki versus the Beemer to buy another entire bike. Or failing that, a lot of oil, tires, fuel, chains, jackets, and helmets.
That, and I do not relish the thought of having to wrench on a modern BMW anything. That's just me.