I think Parade works really well as a musical, having seen it on Broadway twice, in the revision produced in LA (directed by Rob Ashford) from the london revival, and in a regional production. It's not as straight forward or emotionally predictable as other writers might have crafted it, but it always keeps me engaged in the story and characters and themes, intellectually and emotionally stimulated -- entertained and moved. And of course is a memorable and staggeringly good score.
I don't think Last 5 Years can be compared to Songs... one is a song cycle that tells a story between two fleshed out characters, the other is a song collection with sketches of unrelated and unconnected characters and self-contained short stories linked by a loose theme. Very different pieces of writing and experiences for an audience.