I really don't think they are very similar in meaning at all, I'm sorry. Have you tried looking up each one in the Word Reference dictionary and searching for previous threads? I know we had one in which "rich food" was discussed fairly recently.
Thanks, cyclonviv, for your concern.
Based on my poor English instinct, I think a rich meal is close to an abundant meal, while a fancy meal refers to a high-class, expensive, and delicious meal. Am I on the right track?