Of the three, my favorite is Andy Griffith's Andy Taylor.
This may seem rather surprising; it surprises me! For one thing, Andy Griffith, while a notable performer, is not the best actor of the three. So I've been pondering my reaction for awhile, and here is the result of my pondering.
Fred MacMurray as Steve Douglas
I encountered Fred MacMurray in sleazy, amoral, charming bad guy mode long before I encountered him as a good dad. I saw him initially in The Apartment and then in Double Indemnity. He is terrific in both. When I watch him in My Three Sons, I find him believable, but part of me can't help but wonder, "Maybe he's selling bogus insurance on the side."
It doesn't help that I think selling bogus insurance on the side might make the show more interesting.
Dick Van Dyke as Rob Petrie
Dick Van Dyke is a phenomenal performer. The Dick Van Dyke show gave him an opportunity to showcase his amazing comedic talents. And he is very funny. I just don't believe in, well, the entire family. Mary Tyler Moore chills me and their awful whiny son makes me want to turn off the TV (children actors tend to fall into three categories: cutesy/whiny, natural, and too-clever-by-half; I'm not a fan of cutesy-whiny).
Both Rob and Steve do their fatherly duties, but those duties never seem real. Kid has a problem, Dad tackles problem with heart-felt talk. Moreover, both fathers are always perfect in their discipline. Of course, they are right. Of course, their kids come around.
Andy Griffith as Andy Taylor
And he doesn't discipline all that often. His interactions with Opie range from reading to him to encouraging him to dance to participating in his adventures to getting annoyed when Opie asks too many questions. Opie doesn't make random appearances from some back room where he has been stored, waiting for his lines nor is Opie's sole purpose in life to demonstrate what a great guy his father is. He exists as a human being in his own right.
To put it in script-writing terms, Opie participates in conversations--not just conversations with his peers or conversations about his day with his dad or special heartfelt conversations. But actual conversations.
In one episode, Andy is complaining about Aunt Bee's wig. "If a 10-year-old boy can notice it's a wig . . . !" he tells Aunt Bee.
Standing on the stairs behind Aunt Bee, Opie says, "12."Andy doesn't talk at Opie or down to him. Their dialog is off-the-cuff, almost absent-minded. "Hi, Dad." "Hi, Ope." The conversations, moreover, take place while Andy is doing other things like talking to Aunt Bee or getting his hair cut or filing stuff in the jail. Quality smaulity time. Between "sitting down with my dear son(s)" and "yeah, my kid is around even when I'm doing other stuff," I'd take the latter over the former any day of the week. Being a family isn't about taking the kid on a ride; it's about saying, "So, whatcha up to? I'm doing this."
"12-year-old boy," Andy continues.
"I'm starting to like it," Opie says.
"Don't you have something to do?" Andy snaps at him.
The closest equivalent to The Andy Griffith Show is really Home Improvement (rather than the very funny-but-also-a-showcase-for-a-performer The Cosby Show). My Three Sons seems to be rather like Full House.
It does help that Ron Howard was a remarkable child actor. I didn't understand until I watched The Andy Griffith Show why, when I was growing up in the 80s, Ron Howard was seen as America's kid brother, the one who became a director! I understand it now.
Ron Howard falls into the natural category. Jonathan Taylor Thomas, of Home Improvement fame, falls in the too-clever category (and was gifted enough to pull it off). Interestingly enough, both these boys (mostly) gave up acting. JTT has appeared on Tim Allen's Last Man Standing.