Are you interested in Applied Math, Stats, Biostats, or CS? With my extremely limited experience I believe you'll be competitive just about everywhere for M.S. in Stats/Biostats. Perhaps not so much for CS anywhere. Well, contingent on your GRE score and subject score. PhD is a different story.
I think you'll be more competitive at CMU Stats than CMU CS.
It really depends on how PDE/computing theory is taught at your school and how much you'd enjoy learning about the topics... I'd take theory of computing just because I'm more interested in that, but that's just me.