The surface method is more accurate than end area volumes. In saying that though the underlying mesh of points making the surface model is important. The more the better, but with a disclaimer, the surface model needs to take into "Breaklines" making the model more accurate, whilst more points are better, the orientation of the field survey points can have an impact also. We compared Lidar data to real survey data for a road surface and it was very good with +- 20mm but the LIdar was a grid based so bumps and hollows are not taken into account.
One project flood problem, we surveyed an intersection at 1m grids to establish overland water flow, with 1/2 turning left at the intersection and going through a private property.
So if using Google Earth etc its grid based and at what sort of accuracy for Z ? We had photo grammatic levels, then Aerial, then Aerial again for smaller areas at 1m grids. We offered ground survey to be added to the master surface model also. Of course now we have point clouds.