Substance Painter does not support well meshes divided in a lot of individual sub-meshes. It is better to combine meshes together (but not necessarily attach the polygons together), otherwise the application will experience a lot of slow downs. There is no polycount limit however, Substance Painter can handle a large amount of triangles (multiple millions).
UVs can have an impact too. Substance Painter works by dividing a texture/channel into smaller chunks to speed up computations. However this optimization will be made useless if when painting on a mesh in the 3D view, the brush stroke has to be done at different corners of the texture. Grouping UV islands together instead of relying on automatic packing in a modeling software can have a big impact on performances.