Regarding your original stipend question, I'm currently a first year student at Rutgers and living fairly comfortably on the stipend. While 20,000 isn't alot to live off of, you adjust pretty quickly and you will not need a second job (unless you want one). I am able to eat, pay my rent, bills etc. BTW. I love the university.
I've lived in the DC metro area and 14,000 does not seem like it would be sufficient (and I knew a few people there who made off hand comments about it).
To be honest, I'd be less concerned about your stipend and the schools reputation and more concerned with your mentor's status. Go to the school that you would have the better mentor. The one where you perceive yourself to be more productive and have a better relationship with faulty AND other students. Happiness is extremely important in making it through a long program. If you have to take out a few thou. in loans or work a couple hours a week for a better program, then do it.