The foundation around my home is concrete, except on one side. On that one side my builder used insulation, which he said also acts as a drainage board, and he covered the insulation with something that looks like concrete. But if you push against this board, you find that it it isn't concrete - it's softer. Now my landscaper doesn't want to put a retaining wall next to this insulation, saying that the heavy block could damage the insulation and allow water to get into the insulation, resulting in mold, etc. I talked to another builder who told me it's common to use this type of insulation/drainage board. I need a retaining wall, and my landscaper says that I should have the wall covered in concrete. Who's right?

That "insulation" is in fact a drainage barrier to allow water drain down to the footer drain. It is designed to be wet. There is no mold issue here.