A three sigma effect is impressive in just about any branch of science except precision electroweak measurements. I strongly hope that this result is borne out--we've been waiting for chinks in the armor of the Standard Model--but I'd like to see this verified by a method with different systematics, similar to the way the Sudbury Neutrino Observatory complements the (late, lamented) Super-KamiokaNDE experiment.
Offhand, I don't know what sort of theories this result favors. It doesn't seem likely that this is an indication of supersymmetry, because I don't see how it could affect neutrinos but not other currents.