I would test in this fashion.

Find a target with consistent lighting and more or less even lighting. Better yet, use a calibrated grey card as your target.

https://www.adorama.com/dkgc.html?gclsrc=aw.ds&gclid=Cj0KCQjwtr_mBRDeARIsALfBZA71LB0b2e74ChAebOsxQSfOZYrzg2J3gQEdy8L5QIHJ1x4nOju2BrAaAp64EALw_wcB

Using a tripod, set one camera to spot metering and manual exposure settings, and pick an ISO that works. Take some shots, with one lens. then the other, then swap the bodies and do the same.

Your description of your testing seems to leave a few variables - metering, two different lenses but only on two different cameras, auto ISO, etc.

Lenses have different light transmission, and unless you hold all parameters and test for one, you really won't be able to assess whether it is the combination of the D500 and the 70-300 that is requiring exposure comp, or the lens. And by only comparing one camera and lens to another, you will never really know if you have a defective camera or lens.

Another quick check is to compare your settings to a standard EV chart. The chart will have some common scenes and an exposure setting suggestion.

A third way is to go out on a sunny, cloudless day and set your camera for "Sunny 16" and choose subjects that are generally sunlit and preferably average contrast - not women in white dresses standing in front of black limousines. A value of EV15 (bright hazy sun) F16 at ISO 100, 1/125 sec or any combination that works to provide the same exposure - such as 1/250 at F11, 1/500 at F8, etc.

http://www.irismasters.com/exposure-value-table-for-easier-photography/

Any number of things can be wrong - a mis-calibrated shutter, sticky aperture blades, different light transmission between lenses, mis-calibrated meter, to mention a few.

Then there is this to consider:

https://www.dpreview.com/forums/thread/4097249

It could very well be how the D500 handles matrix metering compared to other cameras.