The "Odometer" is no more accurate than the speedometer, since they function using the same input, a mechanical "counter" of wheel revolutions. Changing your car's wheels to a different size, or even mounting tires of different size/specs will change the speedometer's and the odometer's readouts, both of which are set for the tires/wheels with which the car was originally equipped.

The GPS on the other hand will be far more accurate at measuring distance, although depending upon its software, will have a pronounced delay in displaying speed changes and a lesser lag time in reporting distance traveled. Depending on the type and sophistication of the GPS, its monitoring of rate of change of satellite reference points is almost constant.

Even in the days when the technology was young, and the US Navy's GPSs were big and cumbersome, they were far more accurate when used for traveling in confined waters than the best calibrated pit log (a mechanical device which measures hull speed through water) and certainly as good as the best navigation team translating optical bearings to chart positions. Back when the technology was new, surveying groups using GPS equipment discovered countless "landmarks" which were inaccurately located on maps and very precise surveys.

The current models are amazing bits of electronics (but in map display mode, entirely dependent upon the accuracy - and age - of the electronic maps with which they are "loaded" or updated).