I think when comparing the two and especially weighing in which film is better for teenagers to view, Saturday Night Fever is the superior film.
My reasons are as follows:
Grease is a nostalgic-bait view of the 1950s where times seem to be simpler. This is a pretty common trend where media of a generation portrays a story in earlier years as less troublesome. Grease's world is one where white students are the main cast, no allusions to racial discrimination is an issue, rampant sexism is not treated as seriously, and other social issues are not shown. When Danny attempts to rape Sandy, the movie never focuses on Sandy's reaction to be retreating from this event and instead focuses on Danny's song about how much h wants to be true. The final ending of the movie has Sandy change for Danny rather than Danny changing for her.
The 1950's contrary to popular conception, were not a easy-going period. The cold war, poverty, racism, sexism, worries about crime, the red scare, decolonization, rise of pan-Arabism, homosexuality, etc were concerns the country had. To many people today, it may shock you that the 1950s did not have Medicaid or Medicare. The 1950s also saw thousands of Americans out of high school/college die in Korea. Its clear Grease (the movie), was made to present a comforting popularized version of the 1950s to the ww2 generation and the younger generation born out from the 1960s of a "better past."
Saturday Night Fever on the other hand encapsulates more accurately the real-life issues of the 1970s in inner city America. Our characters are working class, trying to survive in a decaying capitalist America where inflation and a lack of jobs are worsening their living situations. More Americans and especially teenagers will face this problem as they grow up; alienation.
Tony, and his male friends, are rapists who never receive their due punishment. Unlike Grease, and more importantly for impressionable movie goers, the film NEVER downplays the horrible events. We SEE the fear and damage the women suffer. We are revolted when John's character, Tony, shames Annette for being raped under the influence of drugs. What is worse is that, in real life, this is too common. I seriously am reminded of Eight Grade's story.
Unlike Grease, the ending to Saturday Night Fever, gives a more ambiguous and bittersweet ending. Tony promises to Stephanie that he only wants to be friends and that he wants to better himself. It's honestly a more positive look at masculinity than anything Grease ever showed and forces us to think at what it means to be break away from a social group that upholds sexism.
And its not like sexism is only confined to women. We see how tony and his friends nearly attack a gay couple while walking in the city. Again, this is accurate to the time period and is still an issue today. Racism is also tackled with Tony and his friends attacking a Puerto Rican gang for an alleged assault on their friend and racism at the dance club competition.
While Saturday Night Fever has been rightfully criticized for whitewashing the real-life disco scene, its strengths I believe overcome its problems.
Plus, if Saturday Night Fever is criticized for misrepresenting history, then why is not Grease?
*As a sidenote, I believe Grease 2 actually may be better than Grease because it similarly has a better message about gender roles than Grease.