gps would give a lateral distacne
Actually, most people don't realize it but GPS is a little more complicated than that. The maximum location finding accuracy of a consumer GPS unit is within about 10 feet. Since you have to measure two points to get the distance between them, the maximum accuracy of any GPS-measured distance is around 20 feet of error. In addition, reception is rarely optimal so good units also display EPE (estimated position error) to tell you roughly how much worse than optimally the unit is receiving signals. Under general use, you can expect accuracy within about 30 feet when measuring a given point, which means +/-60 feet of error for a measured distance.
Also, most GPS units do measure elevation. My experience has been that they are very slow to measure it, and it is usually less accurate than a properly calibrated barometric pressure based unit. I have an inexpensive pressure-type elevation sensor, and it is accurate measuring change within about 20 feet. I also have both a Garmin and a Magellan GPS, and their elevation measurements tend to fluctuate by one or two hundred feet, which makes them useless for measuring elevation change on something as small as a disc golf hole.
There are very expensive GPS systems used for land surveying and such that are much more exact than what I described, but they are not commonly available or affordable. I think if I were measuring a course and wanted maximum accuracy I would use a good range finder and a pressure-based altimeter.