I don't know the programs, but I find changing systems in Markov chains to be more interesting than group theory, although I will admit, group theory is useful in understanding conservation laws, crystal lattices, etc. But recently I encountered a way to use Markov chains to model the long-term behavior of neutrinos in terms of what flavors they are. Really neat stuff!
I'd recommend looking through the publications of the mentors/professors you would be working with, or at least the abstracts, in order to see what may appeal to you more. As well as look at the graduate program to both; one of these very well may be the grad school you want to go to, and having done an REU there will boost your chances of getting in significantly, plus you'd have contacts, etc...