And in response to your question - here's the perspective I've gotten in my similar dilemma (paying tuition at a top tier school vs. full funding at another good, but not as reputable program). Going to Yale has no guarantee of success, however, it does put you in a position to have a lot of doors opened and opportunities presented to you. If you're able to fully take advantage of those opportunities, in my opinion it's worth it to go for it. The question is, is the money piece of the equation going to put you in a situation where your work is compromised in a significant way, during and/or after coming out of the program. If the answer is no, again, I'd go for it if I were you. Just the fact that Yale on your cv gives you way better of odds of securing a good teaching gig in the future would for me equal a solid return on the investment.
This is only though if you think Yale is the place where you're going to do your best work. If being at Rutgers with the freedom to experiment, and not stress about cash would equate to you creating more freely, and the specifics of the program are just as good for you (faculty, facilities, etc), then no reason not to go that route.