Mary Poppins and The Sound of Music

I recently watched The Sound of Music, then later Mary Poppins, after not seeing them for years (the latter much longer than the former).  During this I was of the mistaken belief that The Sound of Music was made earlier than Mary Poppins, perhaps a decade earlier.
So it seemed to me as though, perhaps, Mary Poppins was the psychedelic age's response to The Sound of Music.  It certainly is a psychedelic movie, of the classic British (and "British invasion") variety (another is Willy Wonka, and Alice in Wonderland, and the 60s TV show "The Prisoner" comes to mind).
I think comparisons come easily, but perhaps moreso when I believed that was the chronological order of their creation:
*in Poppins, the house with a sea captain on top seemed like a reference to the running of a home like a ship in The Sound of Music
*at the start, the fathers don't engage much with their children, who want their affection
*both have a series of unsuccessful nannies, and Julie Andrews comes in as the successful one
*In Sound of Music, two women are contrasted and in competition ("is there anything you can't do?" after the puppet play).  In Poppins, it's the father contrasted with Bert.
*similar personality/worldview of the fathers at the start (some Productivity VS Leisure type stuff).  The one in Poppins seemed like a parody of the one in Music.  Unsexy, ridiculous.
Sort of a side note to the comparison:  the cannon blasts at the top of the hour seem intended to comment on the strict timekeeping of Mr. Banks.  Whether unleashing disruptive chaos, or requiring strict order, neither are very harmonious to the people around them (they are both rather imposing, and others around them have to do the work of keeping order).