Congrats @lavafish! I totally agree with you, after more thought my decision goes down to Stanford/MIT. Columbia initially appeals to me due to the opportunity to network in NYC and the program length, but I also have the impression that they have a large cohort and I would very much prefer a smaller, tight-knit cohort. Their curriculum (in terms of length and mix of classes) is comparable to Stanford, so I'd choose Stanford over Columbia.
MIT Sloan's resource for professional development seems outstanding to me (they have perfect placement rate). Another great plus in addition to the two you highlighted is the opportunity to conduct research assistantship with MIT professors. It seems like the MBAn program has great career pipeline if you want to do data science in consulting/finance (in addition to other industries - these two stood out to me, just like how Stanford's connection to Silicon Valley tech stood out to me).
I do prefer Stanford's curriculum in that students get to take more (in terms of units, but also variety) classes focusing on various topics in ML and computing. It is pretty crazy that you can take classes with, and possibly do research with, some of the most influential names in ML (e.g. Andrew Ng and Rob Tibshirani). Another big plus is the opportunity for full-time 3 month summer internship AND capstone project (if you choose to do one for the Practical Component). Also I think last year Stanford admitted ~20 students and MIT MBAn admitted ~50-60 students.
Personally, I'd like to stay in California, hence Stanford ranks higher.
These two/three programs are really, really good options to have and I hope we choose wisely : ) let me know what you decide on!