WARNING: I'm not a fan of Princess Bride and haven't watched it in decades, so take these comments for what they're worth. Aside from the excellent issues mentioned above, it seems to me intent is a big point of contrast between these two works. I'm an English teacher, and English teachers are supposed to love Romeo and Juliet. I don't love it, but I do like it and appreciate it because, among other things, in it Shakespeare reveals so many aspects of human nature (being in love and being impetuous and being secretive and being angry...and the list goes on) which are part of who we are today. Almost everyone I know thinks I should love Princess Bride, as well, but I find it silly and ridiculous. People of all ages quote lines and laugh at the inside jokes from this movie (which of course aren't at all humorous to me), but I've heard nothing particularly insightful or applicable to make me take note. It's funny, apparently, but that's about it. Please don't misunderstand--sometimes a movie or book or play can just be funny or silly or entertaining. But to compare those kinds of works to something which has some sense of depth and longevity is a fruitless pursuit, for me.
The Biggest difference (assuming that you aren't referring specifically to the film adaptation of The Princess Bride), is that one is a novel that was written with the intention that it be read, and the other is a play, written with the intention that it be experienced as performed live by actors.
Interestingly, William Goldman is a screenwriter and playwright as well as novelist, so he is certainly aware of the difference of choosing the novel as his literary form over either a movie or play. He is able, since his audience is reading rather than watching The Princess Bride, to really give the reader a strong sense of his point of view, even going as far as to include is own "asides" in the text. This novel was intended, without a doubt, to be experienced by a reader.
Romeo and Juliet is, on the other hand, a script that Shakespeare, so far as we can tell, never had any intention of publishing to be read or studied. He wrote what are called sides -- portions of the script for each actor that contained that actor's lines and the cue line that came before his. The actors each held their own sides as they rehearsed the plays, and an actor would know how big his part was based upon the length of his sides.
Again, as far as we know, there were no complete scripts of Shakespeare's plays published until the actors' sides were gathered after the plays had been performed, and, in some cases, after Shakespeare's death. The script, for Shakespeare, was meant to provide the actors their lines. The audience then experienced the live, three-dimensional performance, not words on a page.
This difference of genre -- novel versus play -- is, for me, the most important and defining difference between the two.
It is difficult to categorize similarities and differences of these two stories as each similarity seems to present an even bigger difference. Therefore, please excuse the disorganization of the following list:
- Both stories are love stories at the core; one is a tragedy the other is a comedy (with a happy ending).
- Both female protagonists come from wealthy families and fall in love with a man whom their families would likely disapprove of; Romeo is not poor but an enemy, Wesley is a poor farmboy who would likely not be able to provide.
- Both stories include several instances of sword fighting; far more people die in "Romeo and Juliet" than in The Princess Bride.
- Both stories have elements of humor; Shakespeare's humor was more subtle and tended to be based on nuances of word-play and comic-relief characters. Goldman's humor is overt, over the top, and an exaggeration, as The Princess Bride is intentionally poking fun at the traditional idea of "fairy tale."