There are so many differences it's impossible to list them. In general, Postman focuses on having every feature under the sun (integration testing, mock APIs, etc) whereas Insomnia focuses on the core of just being an HTTP client with additional helpers to be more productive. The result being that Insomnia is not suitable for as many use cases but is has a better user experience because it's more focused. Insomnia is also open source software.

You should really try them both to figure out which one best suites you.

P.S. I'm the developer of Insomnia.