I guess GPS versus baro altitude have to be quite close because they are both (simplistically) measuring the distance from the centre of the earth...
Actually GPS calculates a 3D solution in space, which is related to a height above a theoretical shape which approximates the earth's shape (a slightly squashed sphere). This height is then remapped (in any half decent GPS, using either a lookup table or a polynomial surface) onto another theoretical shape which very closely represents the earth's "sea level" surface.
That's why a good GPS will read a very accurate altitude; usually within 20-50ft. GPSs which pick up the EGNOS satellite get even better than that; within say 10ft.
The reason one uses a
barometric altimeter is for vertical separation of traffic.
But if you stood on top of some mountain and wanted to know your altitude, the best thing you can do (without spending vast amounts of money on gear) is a GPS with EGNOS capability (e.g. a Garmin 496). Forget altimeters... they read way off if the temperature is nonstandard and anyway where will you get the QNH to set in it?