Both do durable workflows with similar guarantees. The big difference is that DBOS is an open-source library you can add to your existing code and run anywhere, whereas Durable Functions is a cloud offering for orchestrating serverless functions on Azure.
As far as I know, Azure Durable Functions doesn't have a server-side proprietary component and it's actually fully open source framework/clients as well. So it's actually not a cloud offering per-se. You can see the full implementations at:
* https://github.com/Azure/durabletask
* https://github.com/microsoft/durabletask-go
That's interesting, I'll take a look! I had always thought of it as an Azure-only thing.