I've found when I got the cyclometer calibrated, it's within 1 percent of the GPS and I live in South Carolina on mountain bike tires. If I get lazy and let the air pressure down in the tires, the cyclometer will be off up to 5 percent on the same rides. It's not the GPS that has changed, it's the accuracy of the cyclometer due to lower air pressure and tire wear. Once I calibrate the cyclometer again, it's within 1 percent of the GPS.
Two notes.
1) You got to property calibrate your cyclometer. That means measuring the tire distance and not just using a chart. And especially on thick tires, you'll have to calibrate every so often.
2) If you are in the dense woods, a canyon, or in a major downtown area, a GPS will not be nearly as accurate as a properly calibrated cyclometer. I wouldn't say way off, in downtown Baltimore this year, I estimated it was off by 3 percent after I plotted the course using mapping software.
There's no reason not to have both considering how cheap a cyclometer is. They compliment each other, not contradict each other. The one thing a GPS is when you follow the same ride is the consistancy. I always know when I am going to pass 3 miles on my ride (stop sign)... 5 miles on my ride (last mailbox before turning right to Lake) etc.