I trust Drew more than Payton to stick around. I love him and all, but he is a wild card, you don't know what he is going to do, on the field or off. I don't really think he is invested in the New Orleans community to the point where he would stay here in a rebuilding phase and skip a chance at another ring somewhere else.
Drew on the other hand seems really appreciative of the city and enjoys living here.

That said, they are both from Texas, and if the sign start showing that the rest of the team is breaking down, it isn't outside the realm of reason for them both to look at Houston (I don't think Dallas is a good fit) to pick up where they left off.