Which is more accurate, the display on my speedometer, or the speed display on my GPS? And, which one will be closer to the cop's radar?

Assume you’re driving as fast as the faster readout.

I have ran as many as 3 GPS’s at once and found them to be super accurate at any speed and they always agree with each other, I would trust the GPS.

As usual, Wikipedia has an article about GPS speedometers that says:

Speed calculations will be more accurate at higher speeds, when the ratio of positional error to positional change is lower. The GPS software may also use a moving average calculation to reduce error.

As mentioned in the satnav article, GPS data has been used to overturn a speeding ticket; the GPS logs showed the defendant traveling below the speed limit when they were ticketed. That the data came from a GPS device was likely less important than the fact that it was logged; logs from the vehicle’s speedometer could likely have been used instead, had they existed.

I have no personal experience with a GPS unit. I’ve estimated errors in dashboard speedometers and odometers, however, in many different vehicles over the years—and find them to vary from about 1 to 5 percent error, assuming correct tire size. Not bad for the lowest bidders! Interestingly, speedo & odo errors can be quite different in the same car.

If you’re vehicle has stock wheels and no known speedometer problem, the car’s speedometer will be more accurate than a GPS reading.

The GPS. Mine is always a tad below my speedo reading, but it’s right on with those stationary radars they have set up at toll booths and a few other places. A car’s speedometer is never accurate, because it measures speed as a function of revolutions per minute on the driveshaft. Since the diameter of your tires changes with wear and temperature, and is not consistent as the vehicle’s speed varies, there is always going to be some error.

Your GPS is more accurate while driving on the highway. While driving inside a motorcycle ball the speedometer is more accurate.