If you are comfortable reading the source code for each project that is the most revealing way to see the difference.
Strongly disagree on this. Design can mean many different things. For example in the docker vs podman explanation you gave, you are talking about integration with Linux and adherence to Linux standards, and I agree that with you on that. That's one of the reasons I do prefer Podman over Docker.
However when I think about "clean" in regards to podman-compose vs Quadlet, I think about the user/developer experience. Quadlets integrate with systemd, but as a consequence inherit the design and interfaces of systemd. This means putting Quadlet files into a global systemd folder. This makes GitOps harder since all your projects get combined into a single folder. Also I'm not a fan of how verbose systemd config format is, like the repetition of keys. Seeing PublishPort= repeated for every port mapping looks ugly imo. And every service needs to be defined in a separate file, even if some services are only a few lines of config. Which makes it harder to see all services at a glance.
I recognize this is all my subjective preferences, but this is just what I think when I hear "design".