Well, I'm a Jersey boy originally (until after college) who's lived in all 3 of the states you're looking at.
Where in each of those states does make a difference though.
I lived in Handcock, VT just north of Rochester on Route 101, it was a very small town). I then moved north of Granville Gulf to Moretown (north of Waitsfield). This put me 5 minutes from Sugarbush, which was great.
Then it was Huntington for a month or so (staying with a friend) until I found an apartment in South Burlington. SB was the "big city" but had a lot more to offer (if you enjoy going out to eat, seeing bands, etc). But I haven't been back there in about 10 years. I was working at IBM, so my commute was about 10 minutes, which was great..get out of work, drive home, and either get on my mountain bike and ride down to the lake or throw the kayak on the roof and go downtown on the water and paddle until sunset. I miss those days.
In New Hampshire, I lived in Gilmanton, which is another tiny town, and drove 55 miles one way to work in Salem. I did that for about 8 months until I couldn't stand it anymore then moved to Manchester to be closer to work.
[that was only 2 months, then I moved to Austin, TX which is just like Burlington but hotter, much hotter]
I then lived in Rockport, Maine for a few years. I taught snowboarding and did freelance web design work. Living on the coast was great, but it is very isolated in Maine, because it's a haul just to get back to NH (2 hours to the NH border from Rockport). But if you love the ocean (I do) it's a terrific place, with lots of coves to explore by sea kayak (hey, that's my opinion!)
I'm back in NH now, was in Manchester for 2 years, now I live in New Hampton. It's a small town, and gets crowded in the summer with tourists but I like the quieter lifestyle.
I guess I'm lucky because I work out of the house, so I can pretty much live anywhere.
Internet service and cell reception isn't as good up in New Hampton as it was in Manchester.
Property taxes are higher in NH, but without income tax or sales tax, I think it's not a big deal because you're not losing a high percentage of your income to state tax like other states, and average property taxes are about $4000-6000 for a 1500-2000 sq ft home (of course that varies depending on the towns). If you're paying income tax you're probably losing more than $6k/year of income to that. (if you're retired and on fixed income, then it might be harder to justify living in NH)
Of the 3, I enjoy NH the most, but I always have, even when my family used to camp up here 30 years ago. I think it's because NH has the most diversified terrain. Rolling hills in the south, the rocky coast with and beaches on our tiny 10 mile stretch of ocean. The Lakes Region, where I live now, has plenty of lakes and towns that are very different in flavor from one another. The White Mountains region with MW and all the other peaks and little towns nestled in the valleys. Even the Great North Woods, a definite haul from anywhere, but Moose Alley, the Connecticut Lakes and just being in a remote section of NH makes a weekend trip up there worthwhile.
I lucked out too, because my parents retired to Rockport, so I have a place to visit (I'm actually here right now, spent a week taking photography classes).
Now, if I can just convince my brother to move to Vermont, I'd be set, I could enjoy all 3 equally