ZeaCAD - what is the difference between parametric surface based zcad file and mesh based zcad file?

when should I use one of the other?
are there any disadvantages of one or the other?

while the zcad file supports both parametric surface data, and polygon mesh data, we are preferring the polygon mesh data at this stage. The polygon mesh data has some serious advantages, such as being able to clone an asset and add it multiple times to the scene tree. This is not currently supported with the parametric surfaces. There used to be a performance advantage to using parametric surfaces over meshes, but that is no longer the case. Both methods have roughly the same performance, load times, and file sizes, but meshes are more versatile.

Note: The parametric surface renderer is very powerful and we may find use cases in the future where it provides a clear advantage.

Does mesh based approach maintain the association to underlying CAD entities (face, edge, vertex)?

This will be supported soon in the zcad file, but at this time, the mesh-based zcad file does not provide a link to the underlying cad entities in the geometric modeler.