Considering that B&N's long-term outlook isn't great, my guess is Kindle will be the ultimate winner.
That said, I own a Nook tablet and a Kindle e-reader, and use both regularly. The tablet is useful for Overdrive and Hoopla from my library, while the dedicated e-reader Kindle has much longer battery life and, not being backlit, is easier on the eyes for long stretches. I also find it easier to import third-party books, such as Tor e-books of the month, into a Kindle. So I guess that makes me neutral.
Coexistence is possible. I present again my photographic evidence:
Note the lack of spontaneous combustion or black hole formation when a Nook tablet, a Kindle, and a physical book come into direct contact.
(Incidentally, though I've recently upgraded to a Kindle Paperwhite, the old keyboard model still works great and holds a charge beautifully. It was just showing its age with a few small stress cracks in the plastic casing, plus an occasional issue with page turning, easily cleared. The interface on the Paperwhite is taking a little getting used to, but I like the illumination option, and it's thinner and lighter... plus the cover closes nicely so I don't get coins stuck in it anymore. And since this photo was taken I upgraded to the Samsung Galaxy Nook, which was well worth the price, as it's more powerful and functional as a tablet. I suppose I should update my proof-of-coexistence photo one of these days.)