Barometric pressure is usually accurate to less than 5 meters with even a cheap sensor, provided it is calibrated on the day (A fast changing weather system can trow it out however)
GPS altitude is very inaccurate due to the very nature of GPS. Think about the earth, the GPS satellites in orbit, you and the ground The only GPS satellites you can "see" are those above you. To get accurate altitude, you would need to have a satellite below you - which there are - that you can "see" - which you cannot. Therefore it is easy to get accurate lat/long, and hard (nearly impossible) to get accurate altitude.
The only way to get altitude from GPS (the kind that is useful to a cyclist), is to augment the data from either Barometric source, or location based. Unfortunately the altitude profile data is not accurate enough for most cycling applications.
Although I have not used a Nexus, I rely on a Garmin with barometer when in the mountains - My guess is there is no way a GPS based altitude will be more accurate than barometer.