Depends how you configure your bike computer. If you measure right and calibrate, your cyclocomputer will be WAY more accurate than a GPS.

Consumer GPS only has 3m resolution under GOOD conditions. Add a heavy canopy (as is apt to happen when bikng in the woods) and the resolution gets worse (or it blinks out altogether).

Now add some hills and the accuracy of GPS gets even worse. Yes, GPS can determine your altitude as well. But that ads another 3m or error (under good conditions). You could go down a steep 10 foot hill and the GPS may barely register a couple feet of movement.

Here is a hint to those setting up your cyclo computers. Follow the instructions for marking out a full revolution of your wheel. But make sure you LOAD the wheel. When the tire deforms it decreases the radius of the tire ever so slightly. If you measure without load, your distances will be over reported.