I haven't tried sharing, but Paw saves everything to normal files, so it seems like not only can it be shared, but since it's just text, can easily be stored in something like git for easy management.
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.
[0] https://luckymarmot.com/paw