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It seems like most of the classic spatial function available in PostGIS (i.e. ST_Buffer) are usable with Spatialite, but some others don't seem to be supported in Spatialite (i.e.: no such functions: ST_ApproximateMedialAxis).
Is there a list available showing what is supported within QGIS DB-Manager for example?
You need to look at the documentation to see the list of functions that spatialite supports natively. https://www.gaia-gis.it/gaia-sins/spatialite-sql-4.3.0.html
In general, all the functions that come from GEOS are exposed in Spatialite. However, ST_ApproximateMedialAxis is an example of a function that comes from sfcgal, written by OSLandia, which is a wrapper round the underlying CGAL library. This is how most of the 3D functions have been exposed to Postgis. You have to compile sfcgal separately, or, use
CREATE EXTENSION postgis_sfcgal;
So, unless there is project underway to provide sfcgal/cgal to Spatialite, you will most likely be out of luck.
Other things that will be lacking from Spatialite are other projects that have been added to Postgis over the years by 3rd parties -- raster, topology, pgRouting, pgPointCloud, to name a few.
Furthermore, Spatialite lacks much of the higher level RDBMS functionality that comes with Postgres. This is not a criticism, Spatialite simply has a different use case.
So, you are unlikely to find a one-to-one mapping between the spatial functionalities of the two DBs, except that anything that comes from GEOS will be likely be included.
The question really is what is your use case, what type of queries, how many users, how big a DB, etc.
