Looking at it closely, I see the key difference in funding between Univ 1 and Univ 2 is that Univ 2 has offered two years of coursework at the beginning without teaching, whereas Univ 1 expects TAing in the second year. Univ 2 also promises one more year total of funding, but as you pointed out Univ 1 will probably give TAships to people who are progressing towards their degree. (Of course, it might be possible to win other scholarships at Univ 1 that don't require [as much] teaching.)
Off the bat, this funding difference doesn't need to be a decisive factor for me, since I like teaching. But is it a big difference? Wouldn't it be an advantage to focus just on coursework/laying research foundations in the first couple years without worrying about anything else? Especially since I am switching fields and will need to develop a good base in my new discipline...
Yes, I suspect most grad students would prefer to start with two teaching-free years rather than one. On the other hand, you need to learn at some point how to balance your research agenda with the demands of teaching, so TA-ing in the second year would certainly not be the end of the world. Since both programs are offering you multi-year packages, I wouldn't make the differences in those packages the deciding factor.
Main potential advisor at Univ 2 is going through effort to let me know she/he is excited to work with me. However, I do wonder how it is to work with her/him since she/he seems very busy with outside pursuits. How do I go about asking current students about her/his advising track records? Do I just write current grad students (whom I've been encouraged to contact) and ask, "What's Prof X like?" Is this considered nosy prying or justified due diligence? And even if I get a lukewarm response, how is it possible to make a judgment on a sample of one or two?
You've been encouraged to contact them, so you have no reason on earth not to contact them. You're seriously considering entering their intellectual community, which is in itself sufficient justification for getting in touch. Entering a grad program without talking to the current grad students would be like buying a house without knowing anything about the neighborhood: i.e., a really really bad idea. Contact them ASAP.
As far as making a judgment on limited input, by contacting the current grads you'll be getting a wider (and potentially much more revealing) range of input than you've got now. If you're concerned about making an uninformed decision (and you should be) then that's all the more reason to contact them.
Regarding the busy advisor: much of this will depend on you and your needs. Some people function very well with laissez faire, "stop in once or twice a year so I know you're still alive" advising. Other people need more intensive guidance. One of the things you'll learn from talking to the current grad students is what kinds of students thrive with your prospective advisor and what kinds do not. You can then assess which category you'd fit into.
Regarding the health insurance issue: does #1 offer no family coverage whatsoever? Or is it just that you'd have to pay a higher premium? If the former, then I'd have to wonder what century that institution thinks it's living in - and you should ask current grad students how they handle it. If the latter, then it's really just another factor to throw into the financial mix. As you balance out stipend levels with the local cost of living, take account of the added health care costs of program #1. If after all is added and subtracted there is a major difference in your prospective take-home pay, then you and your spouse need to decide whether or not the more miserly program is worth the financial sacrifice.
In general, if it comes down to slightly better funding vs. a slightly better fit academically, I'd go with the academic fit every time. But as with the location issues, that's an issue that you and your spouse need to tackle together.
Speaking of your spouse, where does she stand on all this? How does she feel about picking up and moving? What will she be doing with herself while you're in grad school? If the answer is, finding some kind of job that will help pay the bills, proceed with caution. And you might want to check out some of the threads on relationships between grad students and non-academic partners. It's not an easy road.
