The most important factors in picking a school are cost followed by location at least in my opinion. I know you've probably heard this before but go to the place where you think you'll be most happy living for the next four years as long as it's not prohibitively expensive(>200K debt). I believe ButImLETired had the same dilemma a few years back so perhaps you could PM her (might be a bit biased lol).
Btw second looks ideally should make the choice easier, and if not at least it'll make for a better thought out decision.
I did actually have this exact same dilemma, and yeah I'm definitely a little biased since I picked Vandy, but I do acknowledge that it was an incredibly difficult decision.
The schools actually seem to attract a lot of the same people- a really big variety of folks with interesting backgrounds, a lot of liberal arts people, etc (to be fair, I think Sinai had a slightly greater liberal arts bend but it may have to do with the people I met when I was there). They also have a very friendly feel. Both places feel oddly "warm" unlike really all the other schools where I interviewed.
I can't really tell you what to do in this case because it's actually tougher than people make it seem. I LOVED Sinai. It was a great fit for me as far as its mission, its patient population and the people I met. However, I've lived in NYC before and I actually hate NYC. It's dirty, messy, loud, I always feel like I'm gonna get hit by a car, and because Sinai doesn't have a campus you really can't escape it. I feel like if it was connected to a nice green campus it would be different, but it isn't. I love college campuses- love the tree-lined streets and little cafes nearby and big libraries and the really sweet academic resources (Vandy has a ton of money, which has definitely come in handy). I didn't like that at Sinai I was basically in the hospital, all day, every day. I'd go home to live with med students, then go outside in the hustle and bustle and walk a block back to school. You don't see very many people who are not somehow involved with Sinai specifically and medicine in general. That would really stress me out.
Academically, I think we're probably pretty close. I don't really think there's much of a difference within the "top 20" or whatever, no matter how much people tell me otherwise, besides research money. I don't think our teaching is any better or worse than the teaching anywhere else on the list. That being said, our hospital is fantastic (I'm sure Sinai is too, I just know our own). We have a huge and awesome Children's Hospital, a brand new critical care tower, a big outpatient facility, a VA on campus and of course VUH. It's a BIG hospital, and we're the only med school to use it so we basically have the run of the place. Our Emergency Department is one of the best in the country and we're super busy cause we have a huge catchment area. We're the tertiary center for just about everywhere in the SE (I've met patients from all over TN, Kentucky, some parts of Indiana etc). Our children's hospital is amazing, and we have the only children's emergency room in Nashville (maybe middle TN?) and we're sent the sickest kids cause we're also the best around. In general, after coming from a college that had a big Ivy envy issue, it's nice to be somewhere you can really be proud of calling your school. No, we don't have the cache of Harvard with the common folk, but really neither does Hopkins and they're not exactly lacking in ego. You tell someone around here that you're a Vandy student, they look at you differently. You tell anyone in the medical community in the SE that you're a Vandy med student, and they REALLY look at you differently. I'd be lying if I said I didn't enjoy that. I don't know that we'd have quite the same experience if we were sharing a tiny island with a lot of other top-notch institutions. We never really compare ourselves to anyone else cause we're it around here.
Now, as for location. I'm a big, big fan of moving all around the country (I came to Nashville in part cause I thought it'd be fun to live somewhere new for a while) so I certainly understand the appeal of living in the city. As I said, I don't like NYC for myself, but I had to live there to realize it. Either way, it's a BIG adjustment. And to whomever said that the "cost difference isn't that big a deal"- that's absolutely laughable. Yes, the Sinai dorm is super cheap for its location. But NYC as a whole IS NOT. It is HARD to enjoy the city when you're poor. Maybe I'm not that fantastic a bargain shopper, but I'm not willing to get on a subway and go heaven knows where to find where the cheapest produce is- I honestly just don't have the time for that right now. I live in a one bedroom apartment (not really an option at Sinai btw, and I really wanted to live alone- this was another huge draw for me) a block away from a grocery store and two blocks away from Vandy. Driving downtown takes me 5-10 minutes and from there you can walk anywhere. Yes, you need a car here. Yes, that's a concession- I had to buy a car before coming here. If you're big on public transport, this is definitely not the school for you. That being said, I get in a car maybe once every 2 weeks to get groceries and that's just because I don't want to carry heavy bags. There's plenty within walking distance of my apartment and Vandy so I never have to drive anywhere, really.
I could tell you about how much I love my professors and classmates and how utterly awesome our administration is, how our grads match anywhere they want to go (yes, including NYC) and how straight up nice and happy our residents and attendings are, but honestly, this may be just as true at Sinai. I love my school and think anyone would be lucky to attend, but I accept that this place isn't perfect for everyone. If you choose Sinai, that's totally a reasonable choice, it's a great school and I struggled with it too.
Let me know if you have any other questions!