Technically, GPS is a more “accurate” system but the real advantages/disadvantages are really more political/logistical. As previously mentioned, the GLONASS system isn’t fully operational. So you won’t get as many GLONASS satellites as you would GPS and you couldn’t rely on GLONASS as a stand-alone system. However, GLONASS can be used (and is used) as a compliment to GPS. The addition of GLONASS measurements can be used to enhance GPS performance.

Depending on how your using the system, there may also be features in your GPS receiver that monitor integrity of the signals you are tracking (e.g. RAIM, FDE/FDI). These features will provide better accuracy by excluding bad signals. [To my knowledge] The degraded state of GLONASS don’t allow similar features in a GLONASS receiver.

This is however a fairly academic question since most systems are either purely GPS or GPS/GLONASS combined systems.

GALILEO is in theory a better system than GPS if the EU ever gets its act together. Due to the rather silly choice of codes for GALILEO the receivers will be more complex and so more costly however by the time GALILEO is functional enough to use on its own that shouldn’t be much of an issue.

Combined GPS/GLONASS/GALILEO systems are already on sale which will use signals from all 3 systems in order to give the best possible position.
Just don’t expect to see any of those on sale in the local electronics store any time soon, the cost is a little on the high side.

The difference between both is also the aspect, that GPS expects more intelligence from the receiver, which in turn made it easier to improve the accuracy with software updates.

But once Galileo starts operation, this will likely replace GPS as most accurate navigation service, at least until the next generation of NAVSTAR satellites gets done.

PS: GPS has also no full coverage… it has even less coverage as GLONASS, as GLONASS has higher inclination orbits. But GPS has a complete constellation, while GLONASS still has many satellite slots empty.

However, there is also some misinformation about GPS given in the previous answers that I’d like to address:

SiriusB said: With GPS satellites it makes more sense to have them in a polar orbit so that they can cover the entire Earth’s surface over time.

Firstly, GPS satellites are NOT in polar orbits. Secondly, a polar orbit doesn’t cover the earth any more efficiently than non-polar orbits. What gives GPS satellites the coverage they do (which is 100% of the earth) is the way the 24+ satellites are distributed in their six orbital planes.

SiruisB said: Also I presume that putting a satellite at the relatively large distance required for a stationary orbit (22,000 miles) would significantly reduce the precision with which the distance could be measured

The presumption is incorrect. The control and space segments of GPS would still monitor satellite positions and update the system accordingly.

urwumpe said: The GPS distance means the constallations repeat every 72 hours, other distances change this.

GPS orbital periods are 12 hrs (11hrs, 56min).

You want to use GPS even at high latitudes, but geostationary satellites are hard to receive close to the poles. Next, you want to have all satellites in a special constellation or formation. When the satellites are all close together in the sky, for example in a straight line or at the same point, the accuracy of the calculations drops as the signals will get the same disturbances because of the atmosphere. Also, the mathematical calculations inside the receiver will not work well then. Then, you also want this constellation to repeat in a good pattern at regular times. The GPS distance means the constallations repeat every 72 hours, other distances change this. Regular repetition patterns mean, that your receiver will have it easier to find satellites and calculate their position, even when the ground station of the GPS fails to update the orbit information onboard the satellites (The satellites don’t know this themselves, you need ground stations for the required accuracy).

Finally, you also have to consider the launch vehicles you can use. Today this is not such a big problem, but for GPS, there had been the Delta II planned, which has tight mass limitations.