We had a similar choice a year and a half ago as we considered taking a job in Worcester, MA, and looked at living over the state border in Nashua to avoid the income taxes as well.
We visited in November and though the leaves were still pretty and driving through Vermont was lovely, Nashua, to me, was old, dirty, dingy, and depressing!!! I couldn't wait to get out of there!!
I don't mind "old" places, but Nashua and Manchester were both so depressing. Part of it was that it was nearly fully winter at the time and chilly, but there were so many large old factory-type buildings visible from highways that had big broken-out windows, worn down places, that kind of thing. Add that to a highway system that is old, narrow, and winding roads and hard to drive at night. Everything was gray and black and cold. Not a good vibe.
Granted I don't know the place any better than that. And we did enjoy Gloucester (though they've had negative press for the "pregnancy pacts" in their school this past year). But there was just no way I'd live there. One afternoon was more than enough poking around for me.
Bellevue, in contrast, is new and hasn't had time to wear out in the same way. Some of that newness is obnoxious, but at least stuff mostly still works and there's no big buildings with broken windows. And there's big trees that are green all year. It feels and tastes clean. The people don't walk around with their heads bowed in the same way. The mountains nearby are amazing. People are less formal. It was no hard decision once we visited both areas within a few weeks of each other.
So, New Hampshire: in a nearby school at least, the girls made a pact to all get pregnant together. In Bellevue, you have one of the top ACADEMIC-performing schools in the country.
Job Opportunities - Bellevue wins, I think. Boston competes but is too far to commute daily from nashua unless you really don't mind a long train ride. Nashua doesn't have the size or population to compete there.
Weather - I give Bellevue the edge because it's not as cold and it's much greener, but it's personal preference.
Cost of living - unsure, probably lower in NH
commutes - both suck

outdoor activities - bellevue wins easily. Not so many ticks and much more dramatic scenery and easier outdoor weather.
visiting places - NH wins due to proximity to Boston.
Try to go visit both places in person if you can. We got both places my husband interviewed with to fly all three of us out and check out the areas in person, and that helped immensely......
good luck!