Wow, this is a really interesting dilemma, and you are correct that each of these 2 teachers seems correct in about 50 percent of the case. If I had the money, I'd actually keep going to both simultaneously. Just remember to adjust your playing accordingly for each. You could then form your own opinion based essentially on a combination of the contrasting information along with skepticism on your part towards both, which will be the greatest impetus in forcing you to doublecheck via Google, etc., just WHO is right in each instance. I say this in all reverence to both of my former piano and voice teachers, but the best learning I ever did was when I set out to the library to prove to myself that they were ALL wrong. In each case, each of these teachers WERE wrong in some areas, but right in others. I suppose most would say to go with the Juilliard teacher because of her great instrument and background, but despite the piece of crap upright, what the Chicago teacher says in stark contrast to your Juilliard teacher's misinformation from time to time, makes the Chicago teacher very valuable. I guess if you have to choose only one and it must be amongst these two, and especially if you are working towards an exam or competition, your better bet would be on the Juilliard teacher. But remember that no one teacher will be right in all areas, so always stay mistrusting enough to go the extra mile and keep doublechecking on info, no matter who gives it, if you want to play the best you can.