I have no doubt FF will have better quality than apsc, and that the AF might be better. But I am curious about your in focus % from the NX1 as what I have seem from other source says otherwise.
Are both test done at the same time? The D750 images looks brighter and too warm to look like anything from a cloudy day, while the NX1 looks like a pic from a cloudy day.
The difference in brightness, contrast and colour balance was also the first thing I noticed. However it is mostly due to the images having an embedded colour profile of "ProPhoto RGB" which probably suits the OP's equipment better than yours or mine. If you load the images in Gimp, for instance, it asks whether to convert to sRGB. Doing so makes quite a large difference. A further improvement can be made with a slight curves adjustment.
Note also that the Nikon images have been cropped or resized from the original 6016 x 4016 pixels to 5000 x 3338 pixels. The NX1 pic. has been cropped or resized from 6480 x 4320 pixels to 3000 x 2000 pixels. So, in effect we're comparing 83% of the D750's resolution against 46% of the NX1's resolution.
The exif shows that matrix metering was used for both cameras. For this type of subject, I would have used centre-weighted or even spot metering in an attempt to get better exposure of the dog's face.
Did you use the NX1 AF tracking? It should show a square covering the dog on the LCD. I have seems example of 3 seconds 45 shots of a moving car with a tele lens with almost no mis-focus, but that is on a sunny day. So I am guess for fast moving object toward the shooter, a tele might do a better job than a standard 50mm range. Also the NX1 has a must deeper DOF than the D750, this might put the NX1 at a disadvantage as well as I believe a narrower DOF object is easier to track. Just my guess, if you would do the test in the exact same condition, the difference might not be as large.
In the Nikon shots, the portion of the dog from front paws to just behind the eyes is sharp. That is more or less what you would want, of course. The grass is in focus only for a short distance starting from just in front of the front paws.
In the NX1 shot, the hind leg (only one is visible) seems to be sharp but nothing else. Strangely, the grass seems to be in focus in the NX1 shot all the way from in front of the dog to behind it. The grass is actually sharper than in the Nikon shots. The shorter focal length of the 16-50 lens together with the APS-C crop factor explain the greater depth of field. However, given that the depth of field covers more than the whole dog, why is the whole dog not sharp?
I was hoping the exif would indicate which AF tracking and AF area modes were in effect but if that data exists, the old version of PhotoME that I have doesn't show it. Given the results, I expect the NX was probably using the default Multi AF without restriction of the AF area. Perhaps the OP could clarify.
I think we need to see more examples with known parameters before conclusions can be drawn. For that purpose, OOC jpegs would be better as some processing has been done on these shots.