I think it entirely depends on what you do during your commute.

A lot of drivers who drive during rush hour feel stress because they get annoyed at the behavior of other drivers. That's terrible for the happiness of the commuter.

Traveling via public transport also gives you plenty of opportunities to get upset over other people. It provides you the opportunity to get upset if the bus comes a bit late.

If you travel via public transport you can do tasks like reading a book that you can't do while driving a car or cycling.