Nikon D600: Are the "benefits" of this camera really worth it over the Canon 6D?

For landscape I'd just use the contrast AF.
Fast moving subjects or shallow DOF benefit from a spread out AF array otoh.

Recomposing not not only shifts the focus plane but also allows for extra unintended movement. The latter is a source of random error.

I wouldn't worry - both cameras are sensitive enough to use battery powered continuous lights or shoot at candlelight.

At the same time I'm not exactly fond of 25k+ on any camera.
Something to keep in mind might be the radio system - some 600EX-RTs (and a ST-E3) are the most reliable and convenient way for "small flash"-photography.