It just has the level polish that's difficult to get in a HTML web app like Postman.
In terms of actual features, I can't live without 'dynamic values' - being able to copy response body values (almost like a pointer) and paste into the header of another request.
I ended up trying Paw when I ran in to some issues with Chrome mucking with my headers (forget the details now, but my whole team was running in to this issue a year or so ago), and haven't looked back. Paw's developer has been incredibly great at responding to emails when I had questions or needed support, and is adding great features like a plugin system. My absolute favorite feature, other than saving requests, is the ability to generate code in multiple languages, but most relevant at the time for me was AFNetworking-specific calls. It's not perfect, but saved me a lot of time when modeling new services.
In terms of actual features, I can't live without 'dynamic values' - being able to copy response body values (almost like a pointer) and paste into the header of another request.
http://i.imgur.com/aY8A0NJ.png
It means that things like auth headers and 'current user ID' are always in sync and current.