Hi - I haven't done the carriage rides but I have hiked several of the mountains in the park as well as lower trails and parts of the carriage roads. I think I'd choose the bridge tour because the views from the mountains can be obscured by fog. Yes, you may have fog below as well but that only enhances rather than hides the scenery.
If it's a great view you're looking for, you can pick a clear day and drive up Cadillac Mountain - the tallest in the park - for wonderful panoramas. That road is closed from December until April 15th but I'm guessing those dates won't interfere with your trip?
Cadillac is also a very popular spot for sunrise-watching!!!