What a nice dilemma to have, Cheapseater! I think it really depends on whether you want to extend your summer, or ease into a beautiful fall.
We were in Smuggler's Notch last September, and although it wasn't robed in peak autumn colors, the hills were covered in beautiful splashes of greens, yellows, oranges, and reds! We loved the landscape and wonderful Vermonters, who seem to be a very special breed.
OBX was another place we "discovered" last year, and we'd like to return. The first week of October would still be quite warm, with a chance of getting hit by storms. Hurricanes have changed my plans last minute a few times in the past, so I learned to always have a Plan B.
It all boils down to, do you want a beach or mountain vacation? Another factor might be if one resort is much nicer than the other?
I think Pam nailed it! If only there were a way to do both!
OBX will be nearly vacant the first week in October. A few years ago, we checked in to a place in OBX on the Saturday before Labor Day. It was very busy and crowded but by 6 PM on Labor Day itself, it was like we had the island to ourselves.
We were also at Smugglers' Notch starting Labor Day weekend in 2017. Smuggs about half shuts down starting Labor Day weekend. A number of restaurants and activities at the resort close until the winter season starts. I would expect the same from other VT resorts.
Early September is too early for fall colors although we could see the beginning of the changes. Except for Labor Day itself, it rained all week. We got up Mount Mansfield on the one nice day but were unable to get to Mount Washington. There would have been no point.
However, there are a ton of things to do in that part of Vermont. The biggest problem is distance -- most everything is a couple hours away. Recommendations: the granite quarry at Barre, downtown Burlington, Montpelier, Cabot Creamery, Ben & Jerry's, any of the many maple farms. The huge Stowe complex and the Von Trapp Lodge are just the other side of the Notch. Take your passports and day trip to Montreal.
If you catch fall colors at or near their peak, all the better. But, you can have a great week regardless and, this being "mud, excuse me, STICK season," you can do it without the crowds.
A question for the OP: If you are in Eastern Tennessee, how are you about equidistant from OBX and VT? You have to be starting someplace else. One tip -- don't even think about traveling through or around NYC on Friday.