I notice subtler difference in the regional terrain than someone from another place might. That is true everywhere. Sheep look alike, except to shepherds.
Driving west, the terrain starts becoming more open in the last few miles before leaving New Hampshire. Vermont is greener, or with lighter green of pasture land rather than forest. There is more slate. As it is still largely forest and hills/mountains, I doubt many would notice the difference. Railroads running north and south start right on the other side of the Connecticut River, and there are more of them through Vermont and on into the Lake George area. I don't think there are any trains in New Hampshire now.
That Green Mountain terrain prevails up to the waterways of New York, that historically-important stretch of near-continuous navigable water from NYC to Montreal. As soon as I got west of Saratoga Springs, though, things flattened out and were even more open. Agricultural land now, showing the first hints of Ohio. Coming from Ohio it would likely seem the opposite, with the impression around Rochester that they were seeing the first hints of New England.