GPS altitude is an absolute altitude, in other words, it tells you your true height above sea level, as triangulated by the GPS satellite system. (Due to the satellite geometry needed for accurate height measurement, it cannot be relied upon for flight operations.)
Your altimeters indicate a pressure altitude. Therefore, when flying through a high-pressure area, GPS altitude should read higher than indicated on your altimeters, and lower when flying through a low-pressure weather system.
DGPS is promising to elevate accuracy levels in the vertical plane far beyond what they are at the moment. In my view, all systems should eventually be adapted to DGPS altitude (or it’s successor), eliminating the need for transition altitudes and levels, altimetry errors induced by extreme temperatures, the effects of high wind in mountainous terrain, and rapidly moving pressure systems. It would also lend extreme accuracy to RVSM operations, and go a long way towards reducing dangerous 'altitude busts' in the approach/departure environment.
It would also save fuel. On long flights an aircraft may transit through several pressure systems, coasting downhill into a low (with regard to absolute altitude) and climbing uphill into a high. Eliminating constant 'hunting' for pressure altitude should result in a small, but justifiable savings.