I believe generally speaking a barometric altimeter (calibrated occaisionally to a known altitude point) will be more acurate than an altitude from GPS coordinates. As I understand it, the issues are as follows:

Correct altitude is measured from the "Geoid" which is the actual sea level gravitational potential surface. Due to variations in density in the earths crust, the geoid is a rather "lumpy" and irregular surface, and difficult to handle mathematically. GPS coordiates are measured relative to a "datum" (WGS84, NAD27, etc), which uses a mathematically defined "spheroid". This speheroid is mathematical approximation of the geoid. How accurate your GPS (calculated from satellites) elevations are depends on how closely the spheroid matches the actual geoid at that particular location. Thus, a GPS derived elevation may be spot on....or may be as much as 100 ft (30 m) off.

Some GPS units include a barometric altimeter, which measures altitude from air pressure. Of course air pressure varies with weather changes. Hence the barometric altimeter must be calibrated periodically at a known eleveation. Bench marks, spot elevations such as mountain tops, etc are good places to calibrate your altimeter. Map contours are subject to their own errors, so while still useful, they are not quite as good for calibrating an altimeter. In general a barometric altimeter, calibrated now and then, will be more accurate than an elevation derived from GPS satellites.