I really like both venues, but it depends a little on when you're going.
Blue Bayou: I really like the atmosphere of the restaurant. It's inside the PotC building (at the start, before the drop, in the "bayou" sequence), so it's on the dark side, but that adds to the ambiance. I've not really noticed much noise coming from the boats; the waving and flash photography is mutual (i.e., I've seen people on the boat and people in the restaurant do both). It's on the pricey side, but I do like the food a lot. The Monte Cristo is only available at lunch, but I'm more of a fan of the braised beef short ribs and the jambalaya. The gumbo (starter) is also very good!
Asking for a water side table is very popular, so be prepared to told it'll add 45+ minutes to your wait. Normally it doesn't take that long, but it might. One note, if you have an 11:30 am reservation (when the restaurant opens), you're very likely to get a water side table. Guests with an 11:45 am or noon reservation will have to wait for that first round of guests to finish before water side tables come open. So in that case, a 45 minute wait is very possible.
Big Thunder BBQ: I love the casual feel of the restaurant and the all-you-care-to-eat ribs. It is entirely outdoors, so you're experience is weather dependent. They do not open when it's raining outside. When it's very hot outside, I can imagine this would also be uncomfortable. There are shade coverings, but depending on the angle, so seats end up in the sun. This is a place I like to go either in the Spring or Fall, when the weather is mild. There is also entertainment; think kind of corny-country. It's fun/funny, but not an integral part of the meal.