Haven't done both either, so no help, but if you post this in the Eastern U.S. forum you'd probably get some response.

Cheers!

Mt.Washington is easier to get to. Katahdin is a long haul.
Mt.Washington has tons of eateries, hotels, ski resorts, etc close by.
Katahdin is out by itself and the surrounding towns are small.
If you get to the summit of Washington in the winter and are bone ass tired, you can just hike down the road.
Katahdin has really cool huts that are open in the winter. Reservations are hard to get and done well in advance. That said, if you get a reservation you will meet some really cool people
You have to hoof it in or ski in to the base of Mt.Katahdin (in the winter).
The stars are amazing in the winter at Mt.Katahdin.
If it were me, I would start on Mt.Washington and then try Katahdin.