Every public API eventually needs to change in a breaking way. How you version it shapes years of future maintenance.
URL versioning
Simple and visible (“/v2/users”), but tends to encourage entire API duplication rather than incremental change.
Header versioning
Cleaner URLs, but harder to test casually in a browser and easy for API consumers to forget to set.
The practical answer
Most teams are better served picking either option consistently and documenting it clearly than debating the theoretically “correct” one indefinitely.