Both have their good & bad to me having eaten at both several times and by chance, both last week/weekend.
Fultons is obviously older than The Boathouse and the "atmosphere" reflects that and is all indoors. Very good food, and expected prices for Disney.
The Boathouse has a great atmosphere and as WEDWDW mentioned, sitting outside is a great spot to have drinks and/or diner as well. There is also an outdoor stage in Disney Springs that has entertainment that can be heard from the outdoor bar area. Of course, the prices are again as to be expected for Disney though at times can be a little higher than even I thought they may be.
Both have great food and I do not believe you could go wrong with either choice. To me Fultons does have a little more selection as far as menu items. But again, to each their own with that. We hang out at The Boathouse a lot at the outdoor bar, so there take that as you may.
Sunsets there are great and even right now in the dead heat of summer it is not that bad hanging out there even during mid afternoon times. If I had to say one or the other, I would go with The Boathouse.