These controversies are largely different from one another. They are similar in a sense because both of them argued that the new sort of music reflected bad values and would have a negative impact on youth. There are major differences, however, in the specific types of bad values that are/were attributed to the music.
In the 1950s, rock music was seen as excessively sexualized. Its beat and its lyrics were thought to make young people overly interested in sex. There were also explicit worries about the fact that rock music was based on African American music.
More recently, the worries about rap lyrics and videos have been somewhat different. There are worries about sex, but so much music today is sexualized that the worries about rap are different. They are based largely around the misogynistic lyrics and the exploitation of women in rap videos. Rap is also controversial because of the violent lyrics and the “gangster” personas cultivated by rappers. These worries about promoting violence were largely absent from the controversy about rock music.