Many factors dictate your final image results, and you already know that. So, if I am using a crop body with a 500mm vs a FX sensor body would I have similar results due to the 1.5 crop increases the field of view when the FX camera has increased resolution? In real life I find the a good crop body a better image grabber choice over all on a super telephoto, but that depends on what your photographing. Even supertelephotos can be used for landscapes and in that case a FX would do wonders for you end results.
If you employ that 500mm with a 1.5 crop body for some close in bird work - that is your best combination.. Considering everything, the FX body may have superior resolution sensor. and less noise but the crop body is simply a leap ahead for filling the frame.
I have both a DX and FX body and use them based on my mood and need, neither is better than the other but in some situations one is preferred - easy answer right?.
The FX body excels at capturing cleaner image files FX bodies generally speaking perform better for landscapes and the wider angle work. FX bodies and FX lens perform with exquisite details for you to crop to your needs. The FX bodies and lenses are meant for high detail wide work in my honest opinion, but I am biased.
While a crop factor camera body excites the "I gotta get close" community, it also is a fantastic platform for all photographic work with the right lens. I prefer the crop body with my longer lens. Just as I prefer my FX body for my wider work. Nothing wrong with either approach that is my choice and I stand by it.
|D500 & 400mm Lens
||D810 & 600mm Lens
|The two images above represent what a 1.5 Crop Body & 400mm vs a Full Frame FX Body & 600mm combination will provide. Pardon the white balance difference, I was in the process of fine tuning the lens. This is for size comparison only, not sharpness. As you can see the two images are near identical in image size to sensor with the 400mm and crop body just a bit larger. Keep in mind the D810 edges in Mega Pixels, and can render images that crop better.
Both FX and DX cameras allow for cross over, do not be afraid to use them to achieve your needs regardless of which is perceived to be better.
The example images help to illustrate possible results when using a lens with and without teleconvertors - While I admit, this is not intended to be any measurement of sharpness or otherwise, simply what the field of view (FOV) differences are with different combinations on different bodies.