Although the DX and FX can use the same lenses, the D750 needs to be switched to the DX mode to "fill the frame" with DX lenses. I have a full selection of FX lenses so I don't usually need to do that but I've done it before on occasion. The FX lenses however are mostly of higher optical quality so there's that. Also I find that using heritage "F" lenses, like the 55 micro-Nikkor, work better some times on my D7000 than on my D750. The brighter viewfinder on the D750 is really nice though for easier manual focusing.

Um... use FF lenses?

Other than getting used to the differences in FOV and DOF, the principles and operations of the cameras are really the same.

This poster is right on the money..  I might add it takes some getting used to how clean images are in low light.  

I came from a D200 to a Canon 6D......  

IIRC, D500 reviews covered the fact that it had some of best (if not the best) noise performance from an APS-C sensor.  So I wouldn't doubt you aren't seeing much difference in normal use.

Some of the other things are the narrower DOF, no FOV equivalence conversion on lens focal lengths (a 35mm lens gives the FOV normally associated with a 35mm lens), and depending upon the body the build quality, handling, and viewfinder may be better (D500 build and handling are GTG as a "pro" DX).  If you picked up photography using a APS-C body, you may need a little time to get used to the wider FOV of FF.

There's a lot of personal preferences in what people like or don't, consider important or not, etc... so a large dose of YMMV.  Have fun with it. 

The biggest difference to me, is that with FX, wide angle lenses are actually wide angle lenses.

You'll lose a little bit of perceived reach with telephoto lenses, but regain a huge margin with your wide angles.  And, it's not necessarily a negative for the telephotos, because on the near end, they'll have a broader FOV with shallower DOF than if they were hosted on a DX; and stepping up to an FX with a higher resolution will allow you to regain the perceived reach by cropping in post processing - whereas, you simply can't widen FOV in post processing.