I think I said this in another thread somewhere, bloke above is correct in saying that GPS isn't a perfect measurement tool without some kind of adjustment. But it is however better than +/-15 metres. Most handheld GPS units will get down around <+/-2 metres.
Using a basic GPS to measure against the quoted distance from tee to pin would probably put you somewhere within 15m from quoted as you would need to know the methods used to achieve the original measurement to get any better.
Using it to measure from where you hit the ball to where the ball stops would be within roughly a couple of metres as it's independent of the course and based purely on the difference in lat and long on a global scale.
Elevation can play a part in the difference between GPS and what you would get from a laser but you gotta be a fair way above sea level for it to really matter in terms of a golf shot and you'd have to be hitting the ball a hell of a long way too.
The best accuracy you can expect to attain with any GPS receiver without a correction method applied is within 15 meters (2D RMS) for the horizontal measurement. Vertical accuracy is within 25 meters. This is typically true for any commercial GPS receiver from any vendor.
The GPS accuracy of less than a 1m is military band, but many commercial units can get that accuracy if it is held still enough for a couple minutes. We used a differential GPS and got some pretty good accuracy with the commercial band.
A few of my colleagues used to work for Magellen, and saw the comments above.