It's a matter of taste. I much prefer Goofy's, but I can see why others might prefer Ariel's. I'm not a big fan of the food at Ariel's; there's not a lot to choose from, what we had was not particularly exciting, and pretty much everything seemed to be loaded with fats and/or carbs. (When we went, my son had meatloaf; he loves meatloaf but found Ariel's meatloaf a bit bland. I had a pasta dish and found it OK but boring. I believed they also offered a cheeseburger, a potpie dish, and around 2 other choices. All meals come with a small green salad, and a choice of deserts. The deserts were pretty good) At Goofy's, I feel like I can eat relatively healthy, and there's something for everyone's taste. (Fairly standard but good buffet fare including roast beef, fish, chicken & pork dishes, lasagna, a variety of veges, a salad bar, soup, desert bar, kids bar area with standard kid's fare, etc.) Ariel's offers a nice location, but it's nice to pay a visit to the DLH during a trip. Both places offer good character interaction, although I tend to like to variety and the interaction of characters at Goofy's better.
I celebrated my DS's birthday at Goofy's several years where they did some special things (for a cost). It was fun, but I don't know what they currently offer. You might want to ask other posters or call Disney and see what options you have for birthday celebrations these days.