Actually, the logic was that GPS is not affected by external influences at all and therefore, overall, more accurate than barometric height. Especially membrane boxes are subject to changes in temperature.
I found that many GPS devices and apps display their data incorrectly or at least suboptimal. My Samsung phone always showed an offset of about 150 feet. When I created an app for it, I discovered that I had to correct for geodetic height myself. Once I did that, the values were very accurate. I am quite sure the 150ft offset you mention is caused by this as well. The geodetic offset in Western Europe is quite big.
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I think it's perfectly normal for a GPS which has a good signal to ouput +45 meters anywhere in Europe. See the image below. The developers of apps usually output the raw data without bothering about this. But if you would substract the geodetic offset of the area you are, the data becomes quite accurate.
Barometric height is based on the standard atmosphere. But the real atmosphere on a particular day is always different. It's favourable for GPS data when these differences tend to be bigger.
In aviation, all altitudes such as the ceiling of restricted areas are referenced to the standard atmosphere. That means everybody is making the same error and therefore the data can be interchanged. Not per se that the error is small.
If you want to measure the amount of meters between an airplane and the hard ground (which unlike artificial ceilings do not care about mathematical models), I doubt whether altitudes based on barometric heights will give better results than GPS altitudes which are properly corrected for geodetic height.
WSG-84 Geoid Height:
https://www.google.nl/imgres?imgurl...9_fAhX_BGMBHaEFC0wQMwhCKAIwAg&iact=mrc&uact=8
WGS84 defines the Earth as an ellipsoid: a squashed ball. This ellipsoid is a pretty good approximation to the mean sea level around the planet, but is recognised as having errors of between -100 m and +70 m with respect to the geoid, depending where you are on the planet.