What a great birthday for both your daughter and her friend! As for dining recommendations, I hope you don't mind if I take the liberty of suggesting one restaurant in each of the two parks you mentioned. I'm not sure which of the two parks you intend to dine in, so this way I can make sure you're covered.
In Epcot, I'd suggest
Teppan Edo. It's a hibachi-style restaurant in Japan where your meal is prepared right before your very eyes. My kids love it! Although...they also love
Garden Grill (also in Epcot) for it's unique rotating dining room and character interaction. Oops. That was two.
At Hollywood Studios, I would suggest the
Sci-Fi Dine Theater. It's themed after an old-fashioned drive-in movie theater. The tables are "cars" situated in front of a huge movie screen that plays black and white sci-fi and monster movie clips from back in the day. The restaurant is dimly lit, which only adds to the fun ambiance. My kids love this one, too!
Whichever you choose, I hope your daughter and her friend have the most magical double-digit birthdays ever!