Two acting parent-child duos that are probably arguable. Henry and Jane Fonda, and Martin and Charlie Sheen.
I don’t think I’d want to try to defend either of the offspring against someone who’s staunchly on Team Parent, but as a gut reaction, I’d definitely be inclined to go with Jane. Charlie, I feel less strongly about.
Sammy Davies Senior, dancer with a few acting credits.
This one is difficult because it’s very niche for aficionados of the blues. I do believe that Shemekia Copeland has surpassed here father blues guitar great Johnny Copeland. Shemekia has Grammy nominations and won many other awards for her multiple albums. She also has a daily show on SiriusXM Bluesville.
And Hugh Gibb, I’m sure.
Another from the Baroque era: Domenico Scarlatti is better known nowadays than his father Alessandro.
I think Rufus Wainwright has had more success than his father Loudon Wainwright lll or mother Kate McGarrigle.
On the acting front:
Robert Downey Sr. was primarily a film director, though he also had a number of small movie and television roles as an actor. By the early '90s, his son, Robert Downey Jr., had clearly eclipsed his father’s fame.
Blythe Danner has had a long and successful acting career; she’s won a Tony and two Emmys. But her daugher Gwyneth Paltrow is likely even more famous than her mother ever was (and also has an Emmy, as well as an Oscar).
(I intentionally put Downey and Paltrow in the same post, as they appeared together in a number of Marvel movies, as Tony Stark and Pepper Potts.)
Her fame in the US may exceed his, but in India, I suspect he’s far better known.
Why would we even count in-laws? An offspring marrying someone famous isn’t the same as having a talented offspring.
Don’t forget Martin Sheen and his other son, Emilio Estavez.
WHAT?? I’m pretty sure I learned that they were father and son at some point back in Weird Al’s early days. Maybe I just assumed it, maybe I misremembered. Maybe it’s my own personal Mandela Effect. Damn. Ya think you know something, and only find out you don’t know shit!
Not forgetting Emilio. I just don’t think he’s approached his dad’s level of fame.
Brian Wilson and his brothers Dennis and Carl (The Beach Boys) eclipsed their songwriter, record producer father Murry Wilson.
Since we’re allowed to include non-musicians:
Alan Hale was a prolific and reliable character actor throughout the golden age of Hollywood, starting in the silent days and going right up until his death in 1950. He appeared in literally hundreds of movies, as well as directing eight. He played Little John, Robin Hood’s sidekick, in three separate and unrelated Robin Hood movies, including the classic 1938 version with Errol Flynn.
His son, Alan Hale, Jr., was the Skipper on GiIligan’s Island. That’s certainly not all that he did, and he has hundreds of movie and TV credits of his own. But I think that as long as Gilligan’s Island is in reruns, he’ll be more famous than his dad.
Incidentally, father and son looked and sounded remarkably alike. Watch an old 30s movie with Alan Hale Sr., and you’d swear you were watching the Skipper. It didn’t help that after his father died, he dropped the “Junior” from his billing for a lot of his career.
Bandleader Richard Maltby, Sr. was a big name in his day, but he’s less known nowadays than his son, songwriter Richard Maltby, Jr.
Similarly (I just learned from his Wikipedia page 
) Jarvis Cocker’s musician father would spread false rumors they were related to the singer Joe Cocker to try and boost his career.
Another non-musical nomination:
Kate Beckinsale may be more famous than her father, Richard. Both actors.
I still remember the rumors that Shania Twain was a descendant of Mark Twain, which relied on not thinking too hard about how Mark Twain got his name.
The Sherman Brothers (of Disney songwriting fame) were the sons of Al Sherman, a Tin Pan Alley songwriter who’s mainly remembered for being the father of the Sherman Brothers.
Elizabeth Montgomery is more well known today than her father Robert.
Then Bonnie Raitt is more famous than her father, John Raitt
And how about acting families?
I would certainly say that Drew Barrymore is much larger in the public consciousness today than others in The Barrymore Family. As an actor, Drew does not compare to Lionel or Ethel, but she’s certainly as well known as they were in their days.
I think it was (probably still is) a common misapprehension. Both of them have the same surname, both play(ed) accordion, both played polkas, and the age difference between the two would be consistent with a father-and-son relationship.