Let's face it Joe Woods is not a good DC. We all could see that here. He may be a good positional coach but not a DC.
Yet less than a month after he was fired from the Browns he was hired by the Saints as their DC. What I think the actual problem was is that he is a DC who runs a zone scheme and the personnel here didn't line up with what he runs defensively. So I guess one could say he may lack the ability to alter his scheme to fit his personnel. Or one could say the FO didn't get him the personnel to run his scheme depending on how one looks at it.
But before one jumps the gun on that, I think they should look at just how many moves this FO made to get the players in here to run Schwartz D scheme. They basically did everything in their power to get him the personnel tailored to run what his specialty is. I think one should ask themselves, did they do the same thing for Woods?