Oh I seem to know who you are talking about. He is pretty active on compressed sensing. I would say if you are sure he is not willing to take you as his student then you probably should weigh Delaware a little bit more because good relation with the supervisor is almost the most important thing to survive a PhD program. Even though the professor in Delaware may not give you enough "guidance" on your research but his team will support you in a different way usually. Also please value his administrative power since he is a department chair which normally means safe funding and excellent networking connections.
On the other hand, school rank does not really matter that much if we are not talking about a big name one nation wide. But again, it is your choice to make a decision. If I were the one to make a decision, I would definitely go with a professor with a nice personality. Well, this is just my opinion.