If I set my cruise control to 52mph (indicated) through some roadworks, a gps app on my phone says I'm doing 47mph.

Which is likely to be more accurate? I realise the gps app will average over distance, which is why I used the example of the constant speed through roadworks. During periods of acceleration the speed will be more accurate I guess.

Your speedo will over read by up to 10%.

Allegedly GPS is accurate on a level road but not as accurate when going up and down hills, though I don't see why it would be less accurate on a hill as it is measuring your location in 3D and so should treat vertical and horizontal movement the same. There is obvious innaccuracy built into GPS (unless your using mililtary equipment or fancy surveying equipment) but as I understand it measuring a rate of change of position should be more accurate than a staic position.

In theory GPS can be more accurate since it has an absolute frame of reference. Even disregarding mechanical accuracy, the fact that the speedo is driven from the car's drivetrain means the RPM->speed conversion is entirely dependent on a fixed nominal wheel radius, which in practice will never be accurate - load, temperature, tyre wear, tyre pressure etc. all affect the effective radius of the wheels so the speedo error won't even be consistent.

That said, GPS quality can vary quite a lot and the kind of receivers you get in phones aren't necessarily all that great, even with the ability to offload processing over the network (A-GPS). Given that in ideal conditions GPS has an absolute positional error of around 2m, a time-averaged measurement of a car moving at a constant seed should be acceptably accurate - certainly my phone seems to be, based on those roadside speed measuring signs. An easy test would be to have more than one GPS in the car and see how much the readings differ.