EXPLAIN shows you how the query is being executed.
It won't always give you a recipe for a solution but it's always useful for an experienced Postgres developer to look at to understand why it isn't performing like you expect.
I still don't understand why the two queries runs faster than a single query. There might be good reasons for that and they might not be able to be fixed but at the same time there might be ways to fix it. EXPLAIN gives you clues.
