Another advantage of BA from the East Coast is the ability to take a daytime flight. Personally I can't sleep at all sitting up (unless very tired or possibly very drunk), and would much prefer being able to fly during the day. Of course that means you'd have to stay a night at LHR and fly to Vienna in the morning, but if you don't mind that, that's the way I'd go.

Otherwise, as others have said, it's really a question of how important a wider seat and an extra 7 inches of legroom are to you. If I had to fly overnight I'd be tempted just to go for the direct flight and sleep it off when I arrived at my destination.