I found this was easier to answer with a bulleted comparison. The main thing is Fax Robot is free for anyone who wants to run it on their own network. Phaxio:

I found this was easier to answer with a bulleted comparison. The main thing is Fax Robot is free for anyone who wants to run it on their own network. Phaxio: - Just an API - More features than Fax Robot API - More expensive - Closed source Fax Robot: - An API and a web app - Less API features than Phaxio (send only) - Less expensive - Open source (GPL)