Hi! Creator of Insomnia here :)

The main differences are that Paw is a native Mac app, paid, and closed source.

Insomnia is open source, cross-platform, and free to use (although there is a paid plan).

Some of Insomnia's biggest differentiators are it's GraphQL query editor (autocomplete, linting, etc) and it's ability to be customized via plugins and themes.

That face-off could also serve as a case study of platform-native GUI (Paw) vs the much-maligned Electron (Insomnia, Postman).