I don't think it's that tough of a question, really. Especially considering Marxism SUCKS.
Okay, so, to explain... Functionalism is a theory by Durkheim that says that everyone and everything in society serves a function. It describes the roles each person places (employee, student, parent, etc). Functionalism also describes how we are socialized and begin to learn the norms and values of society through contact with others in the society to be normal people. So, basically, it explains what functions we serve and how we've become the way we are.
Marxism is a more retarded theory by some freaky communist who predicts that the workers of society will realize they're being exploited and resort to communism. He thinks capitalism is the root of all evil, blah, blah, blah. He's crazy. Like, Marxism isn't even worth explaining. But because I have to, it's just: Capitalism is the spawn of Satan. Workers are exploited by the rich. They'll overthrow them. Communist, classless, "equal" society results.
That STILL hasn't come true and it's nowhere near close to how our society is today.
So functionalism FTW.