Priti,
So you are not actually comparing 2 like things.
Mickey's Backyard BBQ is a dinner show. My family enjoyed it quite a bit, and the food was quite good.
Fantasmic! on the other hand is a fireworks and character show at Hollywood Studios, but it is not a dinner experience, per se.
What might be confusing you is that there is a program that combines this show with some of the restaurants in the park. The
Fantasmic Dining Experience offers (at no added cost) is a meal reservation at one of a select list of Hollywood Studios restaurants with a pass that gets you into that evenings Fantasmic! show in a special seating section.
The seating section is not necessarily the best in the theater. It is not awful, but it is not the best. Second, you still have to wait in line. I would recommend still arriving a good 30 minutes before show time during slower seasons, and 45 minutes to an hour ahead of time during the busier times.
Mickey's Backyard BBQ is a buffet (quite good, actually), at picnic tables in a
covered outdoor seating area. There is a live band for entertainment,
along with Mickey and friends who dance with kids. No autographs,
however.
You really can do both. I think that your son might enjoy the BBQ. My kids did. As for Fantasmic!, it is a great show. But I would eat wherever you want, and only use the Experience package if one of those restaurants is where you want to dine.
Have a magical vacation!