I’ve always assumed that there was some sort of connection, but never knew what it was. Apparently neither did Mr. Asimov
(who I am now trying read for research into my wedding project), who speculates that either Shakespeare was working on the comedy version and decided to try his hand at telling a more serious version … or that he’d written the serious version and now wanted to poke some fun at himself. Once Mr. Asimov has answered a question (in this case as being unanswerable) I no longer have motivation to waste time trying to answer it myself :).
But it does offer up a place for opinion. What do you think the relationship is between the two plays, in Shakespeare’s mind? Was he working on them both at the same time? Which came first, and fed the other? Or are they really independent and the overlap has more to do with the common source material he drew from, nothing more?
Personally I like to think that he did R&J first and then satirized himself in Dream. But I have no evidence to back that up one way or the other.