Which is more accurate for height measurement: GPS or barometer?
For surveying glacier movement, or a mountain range's growth/decay, GPS is more accurate.

For airplanes: refresh rate, reliability, and simplicity matter more. When it comes down to accuracy, ground augmented GPS provides ILS CAT I accuracy using LPV. So alongside refresh rate, and accuracy, comes the question of application. For airplanes in cruise, where separation matters, reliable devices are best.

GPS signals can be jammed. As can be seen in the news lately in California and Egypt. And GPS signal can be lost due to ionospheric interference. So, any equipment that doesn't rely on external sources is safer.