Compared to a properly adjusted altimeter, I agree the altitude function of the GPS will have the most error; however, unless you get a high end altimeter that automatically corrects for local pressure or unless you manually adjust the altimeter pressure each time you get in the vehicle and every 100 mi or so (the indicated altitude will also not be corrected for density changes due to temperature or humidity), I suspect the GPS will be about as accurate.
The GPS standard is that 95% of the time the displayed altitude will be within 15 m or about 50ft if the GPS receiver has a unobstructed view of the sky. Usually the reading is more accurate then 50ft but you can't count on it. The other 5% of the time, the displayed altitude can be off by almost any value. That is part of the reason that aircraft GPS approaches are considered non precision with a typical height of 600ft AGL and must be abandoned if less receiver locks can not be maintained continuously with 5 GPS satellites.
FWIW, aircraft altimeters are considered accurate enough for use as long as they are within 75ft of a given known altitude.