Pushpin author here. The main difference is that Pushpin's client-facing protocol is completely defined by the backend server(s) running behind it.
The Nginx Push stream module exposes its own client subscription protocol. For example, clients connect to Nginx and specify the channel they want to subscribe to. With Pushpin, channels are specified by the origin server when responding, so that clients are not privy to channel schema (nor do clients even realize Pushpin exists).
That said, the Nginx module does offer a good amount of control over paths/formats, and I know there are some neat tricks you can do like redirecting a request to the push stream module (I believe Fastmail does this) to achieve protocol control similar to Pushpin.
