Do not give up on encoders. They are a great complement to GPS. I don't know what precision you want to reach, or what terrain your robot will operate in, but wherever it will be, encoders will give you good information about momentary position changes. Of course it will have some error, but when measured over small time period (i.e. 1s) it will be typically much smaller than accuracy of even DGPS.
The problem is encoder error will accumulate over time, so eventually your robot will end up in a completely different position than it should. That's why you should use your GPS data to correct data from encoders (possibly using Kalman filter). Check out this great answer about a sensor fusion.
Benefits of using GPS + encoders:
- GPS signal may be lost (indoors, tall buildings nearby, tunnels, etc.) - how will you know where are you then?
- Even when you lay down your GPS receiver on a table, the position will slowly drift around some central point - data from encoders may be used to correct for that. This is also the reason why you can't use GPS data to calculate distance covered by the robot (not with a ~1m accuracy at least)
- encoders are useful to controlling robot speed, and making sure that it drives straight (which is very hard using open loop PWM)
GPS vs DGPS
Remember that accuracy of i.e. +/- 2m doesn't mean that you will have a constant offset from real position to the north, or any other direction. The readings will float around some position. That's why I would suggest going for higher precision modules