I've been working in this area and I do generally prefer Cartopy over Basemap. Our team recently made this switch. Cartopy is more Pythonic and has a better software design. It has nice abstraction for dealing with and using different map projections. It also handles seam issues well (I cannot recall if this is a problem in Basemap or not). All that said, Basemap has features that are lacking in Cartopy (e.g., can you label lat/lon lines on non-XY projections in Cartopy? The last time I looked, this was not possible.) Also I agree that Cartopy documentation is somewhat lacking in some areas. But going forward I would probably choose Cartopy, notwithstanding Jeff's great work over the years.
