PBR materials WILL export from MAX into the *.fbx file format. But, you must make sure that this option is checked in the FBX Exporter. It is not enabled by default - you must enable this option.
PBR materials will not export into *.obj file format in any meaningful way. The *.obj file format carries limited material information - just "diffuse", "specular", "bump", "opacity", "glossiness", "ao". An *.obj file is made of two parts: the *.obj object itself, and a *.mtl" file that lists the material files associated with the model and describes how they are applied to the vertices in the model.
Some exporters, including the one in MAX, will create the *.mtl file upon export, but in MAX, you also must enable this option. Some exporters will only export the *.obj file and will not create the *.mtl file.
In general, when making an *.obj file for other people to use (as when making a product to sell here), the professional practice is to obtain a good *.obj editor, export the model from your 3d model-building application, and then rework the *.obj files in the good *.obj editor to make sure that all the PBR materials that can be applied to it are applied correctly and completely. (That is, the ensure that the associated *.mtl" file is complete as possible.) Any material files needed by the *.obj model must be in the same directory as the model file itself.
My preferred practice for my products is to include an additional set of folders for each PBR material set used by the model. That is, all the material mat files that can be hooked to the *.obj file are in the top directory, along with the *.obj and the *.mtl file. (In this way, any user can execute or open or import the *.obj file, and it will load and display all of the files that the *.obj format is capable of dislaying.) But, since a purchaser may buy the *.obj model, but actually have some sophisticated rendering engine or modelling software that is capable of displaying all the *.pbr mats (mats such as *.metallic, *. roughness, *.emission, *.specular level, and those things that go beyond what the *obj file format can host), the purchaser will be able to find the complete sets of PBR files also in the product. Then, that purchase can buy the *.obj file, but use it in something ore sophisticated.
Is this explanation clear enough?
