The verdict in one paragraph. Choose Obsidian if you think in links: your notes stay plain Markdown files in a folder you own, the editor is excellent, and a plugin exists for almost anything. Choose Joplin if you want everything open source, free end-to-end encrypted sync through Dropbox, OneDrive or Nextcloud, and an Evernote-style notebook with a web clipper. If what you really want is notes that are private on a Mac and an iPhone, locked with Touch ID or Face ID, with no setup and no account, Dash (which we make, and list last) is the third option.
Both apps are free to download and run offline, so the choice comes down to three questions: do you want plain files or a managed database, how will you sync, and how much do you enjoy configuring your tools?