I don't know about all readers, but from what I have seen in my personal life, involving my friends and family, no one seams to read classic books any more, if at all. Some of my friends, and none of my family have never picked up a classic. I think that readers should mix the two with an even dosage of modern and classic.
In my personal opinion, I find classic literature to be better than modern. The tend to be better written, the stories are fantastic, the characters, the ideas, the philosophy, the language. They are better to me. Back then most books were meant to be read for the enjoyment; for the adventure. If you got some other meaning behind the text, weather the author meant it to be there or not, good for you. You are a free thinker.
Modern books to me lack in a lot of ways. Some of the modern books are poorly written, the stories are mostly cliche, there are not a whole lot of original, or bold ideas, and they don't leave any thing for you to think about usually. They tell you flat out in the book what they mean. They don't let you figure it out for yourself. "The Time Machine" by H.G. Wells could have a dozen or so hidden meanings. Hunger Games tells you exactly what they mean, and don't let you think about it. It isn't riveting.
That being said, there are a lot of good Modern books. They are good for the same reasons a lot of classic literature is good. And some classic literature wasn't all that great either. It is a matter of opinion. I just think that readers should have a good combination of the two.