I am referring to the 2 bus stations you mentioned. The term "edge of town" is an old term. It means that when the new bus station was first built, it was considered at the edge of town. In the years since, Playa has grown up so much that the "edge of town" station is almost as central as the old station near the Cozumel ferry. Some second class busses and the shuttle that leaves every 10 minutes for Cancun, still leave from the old bus station near the Cozumel ferry.
I would spend the night in Playa Del Carmen before a flight from Cancun. The prices are cheaper in most cases, plus there is more to do with a pedestrian zone downtown with shops and bistros. There is so much to do and see on the 5th Avenue, its more than one night's entertainment.
I love to visit Playa (but wouldn't want to live there). We go there when we're needing a taste of civilization.