I thought it was common knowledge that UChicago really likes their ED students while most of the extra early admits at Ivies were athletes, development admits, and legacies. It’s position as an “Ivy backup” and recent commitment to play the ranking game has made it the only school in the US to have an ED 0 round - I can’t see a school doing that. Indeed, every (unofficial) source I could find seems to support that notion.
Another potential factor is that Princeton’s need blind status will not take into account OP’s ability to pay, whole UChicago’s need aware process will take that into account as an advantage.