I see a lot of people comparing Canon and Nikon and discussing high ISO performance, and having access to both systems, I've taken some sample comparisons for those interested. Keep in mind that the Canon 6d came out almost two years before the Nikon D750 did. Both cameras are equipped with their own sigma 35mm 1.4 art lens. All files are untouched raws converted to jpeg with lightroom's default settings (adobe standard profile). Note the differences in color saturation in the raw files.
Here you go! Click any photo to see a full resolution export.
D750 ISO 6400:
6d ISO 6400:
D750 ISO 12800:
6d ISO 12800:
D750 ISO 25600:
6d ISO 25600:
While I won't say that there's no difference because there is, It isn't very significant. Overall I still prefer the Canon files due to their richer colors and contrast as a starting point, but each to their own!