I've only tried .stl directly through Fusion 360 and .obj through the web interface.
Both do not maintain the object/body/component structure and mangle everything in a design into one mesh.
.fbx through the web interface take a few minutes, but it maintains the object structure and brings over a material of sorts from Fusion 360.
That is indeed very nice!
Just to be clear in case you are not aware of it. All of the above are triangulated meshes and am not sure how to control the resolution of that mesh when exporting into .fbx.
@jeff_strater is that something you can help answer?
Edit: If your client is familiar with the render engines (Eevee and Cycles) in Blender, he's definitely correct! That does not at all mean the render results from Fusion 360 are bad and there is definitely the advantage of a fully integrated render engine, but for specific needs, there are better tools available.
For example if you want to do an interactive presentation in real-time raytraced quality, Blender's Eevee render engine is a phenomenal tool.