Don't buy into the "FX is always better" myth - it's just not true. It really depends on what you're shooting. You want to choose the right tools for the job, plain and simple. If you're focal length limited, DX is a really great choice - it's also a bit more compact and the dedicated DX lenses are more compact as well. On the other hand, if you shoot really low light, enjoy shallow depth of field portraits, or photograph primarily city and landscapes, I think FX is can be a better choice. Horses for courses and all. I use my D7200 all the time for wildlife, but when I'm out shooting landscapes or at night, it's my D810.

As for quality, keep in mind the D500 is closer to 21MP than 20 - and the difference between 21 and 24 is negligible. Also the D500 will have a newer sensor and presumably better ISO performance and maybe better dynamic range. In theory, it should get a bit better results, although I think you'd be hard pressed to see it at lower ISOs.

Also keep in mind the D500 is aimed at action shooters. 10FPS, huge buffer, and killer AF is great for action, but if you're shooting just landscapes, those features just don't matter. So, my advice is go D500 if you do action, but if it's mostly stills, don't spend the extra on features you don't need.

Finally, here are a few shots from my D7200. I don't think shooting either the D500 or the D750 would have improved these. So, don't get too worried about what body you're using, just get out and shoot :)
(as always, these look better if you click download)