I don't know about the units discussed at the start of the thread, but the eTrex vista gives a barometric altitude reading, with a calibration feature that, eventually, brings the barometric reading in line with the GPS satellite-calculated elevation. But that calibration can take a while, and in the meantime you're off to somewhere else.

Both the barometric and the satellite elevation are subject to a lot of fluctuation. I have sat in one spot and watched the satellite-calculated elevation change more than thirty feet, in just a few minutes. Altitude readings are obviously harder for the satellite-based system to calculate than latitude or longitude.

You just can't expect a handheld altimeter to be accurate within such a small distance, particularly not if you move. Even the altimeters they put in airplanes are not that accurate. So if you want to know the true elevation change, your best bet is a topographical map.