Never been a student at UChicago, but judging by their MS alumni placements on the program website, normally 2-3 students continue their study in their PhD program in statistics, plus a bunch of other PhD programs at other departments (computer science, economics, business school). Students get into prestigious schools such as UPenn, Yale and Princeton as well.
I know UChicago ms has a larger program size, and some of these students are actually undergrads who completed master-level coursework, but I would say generally UChicago has a better MS placement than UW regarding PhD application, especially if you want to do your PhD in a top-tier program.