Short answer: A lot. At Flynn we're building solutions to what we see as the big problems that developers will face in the next few years. Deis seems to be solely focused on Heroku-like featureset.
Flynn runs anything that runs on Linux, including stateful services like databases. In fact, we package major open source databases as "appliances" that run within the Flynn cluster for ease of use.
Deis has historically required users to use very specific technologies (initially Chef, and now CoreOS). Flynn does not rely on a specific Linux distribution or configuration management system. In fact, Flynn was designed to be modular to give users the greatest possible choice of components (Deis uses a few components we created for Flynn).
Flynn is designed to be a single toolkit that lets you run everything, not just twelve-factor stateless webapps.
We have created a lot of new technology where necessary but we also use off-the-shelf components like CoreOS's etcd, which Deis also uses. Neither we nor CoreOS consider etcd production-ready, and we don't consider any platforms (including Flynn) production-ready until etcd and all underlying components are stable (Deis also depends on the CoreOS alpha channel).
When you see a "1.0" release from Flynn it will come with our full confidence in the stability of all of its components. We also aim to go well beyond what's possible in Heroku today.
From the outside, not much. Both model the Heroku-style workflow with application deployment.
Asides from Deis being production-ready and tacking on a few extra features like `deis pull` and Dockerfile deployment workflows, we take a different approach to our components. We use the best-of-breed components from other OSS projects and focus entirely on the application deployment workflow. Flynn is focused on building the platform from the ground up. They provide the network equipment and messaging primitives (layer 0, as they call it) as well as the platform itself (layer 1) completely from scratch. Deis uses common OSS tools such as nginx and ceph to provide our layer 0 and part of our layer 1 for us and focus entirely on using those components to serve our needs.
