If you haven't already, it might not be a bad idea to see if you can find out where UCONN math PhDs are ending up. Here's a link to their PhD alumni page: http://www.math.uconn.edu/degree-progra ... hd-alumni/
. You can use the dissertation titles to figure out which of them were doing applied math research. I'd try googling their names to see if you can figure out where they ended up. Ideally the ones who graduated within the past 3-4 years are doing post-docs somewhere, and the ones who graduated longer ago than that have faculty positions at places you want to work. If you find that almost nobody is ending up in academia, that could raise a red flag that they didn't place very well (though it could mean they'd rather go into industry, but that tells you something too).
Also, from my (limited) understanding, Stony Brook's applied math has a heavy bent toward finance (hell, who wouldn't being in New York). Knowing that, I'd imagine they're placing a lot (perhaps most) of their alumni in the finance industry. Also, their applied math department is separate from the pure math department, so their rankings are separated. The ranking you have is Stony Brook's pure math department. On their website, they claim they're the 7th ranked applied math department in the country (not sure what rankings they used).
On the other hand, if you're really that comfortable with UCONN and that uncomfortable with Stony Brook, that may be what really matters. If you ignore ranking for a second and think about likelihood of doing well in the program, you'll be more inclined to excel at a place you feel comfortable at. Being miserable for 5 years can take a heavy toll on you, which will no doubt be reflected in your research, and your research is arguably the number one determinant as to whether you can land a solid post doc, and later an academic position. And worst case scenario, being miserable can lead you down the road of hating graduate school and possibly dropping out all together. Say what you will about rankings, but there's a lot to be said about fit.