In a nutshell:
Positioning/navigation apps in general only process the accuracy/precision values passed to them by the GPS module of the device, and they are primarily dependent on the capabilities of the built in GPS chipset (oviously, being indoors or near/underneath obstacles will equally effect the signal strength and thus the accuracy).
You should find sources on these parameters for the smartphone in question on the web, and there are e.g. external GPS modules that can be connected to your phone, similar to high accuracy GPS devices.
However, this might be highly interesting, since it seems there´s progress underway...