A warning: Math 525 may turn out to be not much different than 425, depending on who you're taking with. Nowadays, I believe that most sections have no touch on Measure-theory related stuff. If you want that, go for Econometrics. The end should be either Markov Process (Intro to 526) or Monte-Carlo Methods.
That said, the biggest difference is only for the "rigorous" introduction to concepts for convergence (a.s, in Probability and etc), which should be taught in STATS 426 but at lease mine did not do that. Most schools will do convergence stuff in the second Mathematical Stats class (i.e our STATS 426 version).
Thus, once again, I highly recommend Math 526 over 525, based on who are teaching the class. You would be able to suceed in 526 without 525.
Some other info: In the past, Math 490 was easier than 525, but it seems to change recently because of instructors.
Good luck on your choices!
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