What do you mean by “clean design”?
If you are comfortable reading the source code for each project that is the most revealing way to see the difference.
In short, Docker has a lot more code because it duplicates a lot of kernel and systemd functionality (often poorly), uses multiple components that communication over grpc with each other to do things, requires setuid binaries, and defaults to running everything as root.
Podman, is a straight forward clean simple program that fully uses kernel and systemd interfaces rather than duplicating functionality. Quadlet is build on systemd generators and its use of templates via systemd instances lets you use deterministic dynamic configuration in ways that is unlike anything in Docker.