I suspect that it depends.

Any wheel driven odometer depends on how accurately you have calibrated the instrument and how precisely you ride the exact route. Any tiny error in calibration gets added over and over again so the longer the course, the more your distance will be off. In my road running days I was surprised by how much the elite runners cut every corner. On a curvy course, that can add up to several percentage points of difference.

A GPS determines distance by triangulating satellites in space. Over a very short distance I'm thinking it will be less accurate than a wheel driven odometer but, as the distance increases, the error between the starting and ending points only gets counted once.

Here's my question: "How accurate do you need it to be?"