Well, we have been going to Vermont and New Hampshire for many, many years and own a timeshare in both for 2 weeks summer (and one week spring/fall floater). I am partial to Vermont, but I do like New Hampshire a lot too. I am a member of the VT251 Club (goal to see very town in the state of VT) and have been through 181 towns so far, so I have seen a lot. There is a lot more to see and do than you would think if you research it out. My favorite area is the Lake Champlain region from Charlotte up through Burlington, St. Albans and the Champlain Islands. We stay at our Smuggs timeshare and we head out for everything from there for day trips. You can even take a trip into Canada from there- Montreal and Quebec Province. Stowe is close to Smuggs. The "Notch" is something to see and Mt. Mansfield. There are other timeshares in VT also. Trapp Family Lodge in Stowe. Jackson Gore in central VT, etc. Southern Vt has it's charm as well, but I think there is more to do up north. We have rented a cottage on Lake Champlain also through Home Away. You can even take a ferry across the lake to the NY Adirondacks. You might want to get travel books on both states so you can see how much there really is to do and see. An Explorer's Guide to New Hampshire and an Explorers Guide to Vermont are my favs.
You have to realize that in states like VT and New Hampshire- they are extremely rural and no matter what you have long drives to get to a lot of places.
My perspective is that New Hampshire is more rugged (think high mountains) and Vermont is "softer" (think farms) in terms of topography. Each has it's own vibe. I think it is actually a bit less expensive to vacation in Vermont than New Hampshire. NH has (high) fees for everything where as in VT there is a lot more to do for minimal or no fees. New Hampshire has no sales tax, but both VT and NH have high luxury taxes on lodging and restaurants, etc.
In New Hampshire, we own at Pollard Brook in Lincoln in the White Mountains. It is in a nice central location in the Western Whites near Franconia Notch, the Flume Gorge, Lost River, Echo Lake, Mount Washington (cog railway or auto road), the scenic "kanc" hgwy.(which you can take over to North Conway on the Maine border), etc. We have gone to Lake Winnepausauke from there many times. Some are still long drives though. Other resorts in Lincoln are South Mountain and Loon.
You can stay in one of the states and go into the other maybe for a day trip- but it is a drive and it really limits you as to where you can go and what you can see or do.