Well if you want to answer questions on any sort of game show or quiz, classical literature is going to work out a lot better for you. Similarly, a knowledge of classical literature will put you on good graces with college professors.
Knowing modern literature would help you know what subjects are current and what styles are popular, which would be really helpful if you're a writer.
But in the end, I think a mix of the two is the best answer. Classical literature gives great perspective on the past and why the greats became great, and modern literature keeps you grounded in the present and doesn't limit you to books that survived the test of time. (Wonderful books can easily disappear, so get them while you can.)