Hi Chris,

I’ll approach your question from the cinema point of view, and wanted to share here an interesting interview of Dicaprio about Shutter Island.

Dicaprio says in the second part of the interview that while preparing for the movie, they were watching together great movies with close subjects, and he was amazed on how much Scorcese stored in his brain about cinema and its history in depth and quantity. He says that the amount of cinematographic wealth Scorcese has makes it unfair  to the other directors. I find this phrase extremely revealing as to your subject. Here is the interview:
http://www.allocine.fr/personne/fichepersonne-12972/interviews

Julie, Thanks for this interesting interview. The way Dicaprio laughs when he says this phrase about Scorsese’s wealth of knowledge making it unfair towards the other directors  implies the great competition, and how Scorsese knowledge propels him in the front. To get back to Chris’ original question on what we are missing out in not being exposed to Classical music, great literature and movies, I think that being poor or rich  (not moneywise, but the way Dicaprio expresses it), means to be in the back or in the front. Educating ourselves to be rich in every field is a way to be in the front, to be great, and to store beauty within ourselves.
If you will ask for my preference, to be rich or poor, my answer would be fast and decisive. I’d like to know as much as I can, the wealth of each field feeding who I am, what I’m doing, and my general understanding.

I don't know that any particular genre or sub-genre is more important that another (except, if you want to be accepted within your particular group--you should be cognizant of what that group knows).  It seems to me that exposure to, and study of, a wide variety of art (in the generic sense, not a specific medium) will generally help make someone a better thinker.  I like the reference to Scorcese and his wealth of cinema knowledge.  I think the same can be said of many great musicians or painters or physicists or physicians or whatever.  Having more knowledge and experience helps to think about and understand more things in more ways.