In this film Johann competes against his father for his music, I can't remember all of it, but at the end Staruss Jr says he will only play his music and not his fathers' and all of Vienna then knew it was he who wrote the music, and not his father. He plays all of his walzs and plokas, I do know the movie is NOT called The Great Waltz, as I just bought this one and it's good but not the one I'm looking for.

Can anyone help please?

If you are sure about the time frame, I think the reason you might not be able to find the movies is because it was part of the Walt Disney television movies series. Please check this link: "Walt Disney's Wonderful World of Color" The Waltz King: Part 1 (TV episode 1963) - IMDb

If it is not the Disney one, perhaps this television mini-series from the early '70's is the one you are thinking of: The Strauss Family (TV mini-series 1972) - IMDb

If the links aren't enabled, copy & paste. The links are from a movie database web site. You can read the synopsis & reviews to see if one or the other is what you are looking for.