Just from my personal experiences, playing music is far more distracting when studying.  I prefer silence, but that is just personal perference.

The lone exception is, when I was in college, I came to discover that really hard techno/trance music was extremely beneficial for writing.  I know this is bizarre - but hear me out.

One of the major problems with listening to popular music when attemtping to concentrate is that your brain gets caught up in the "catchy" aspects of a song and your brain recognizes the repetition and diverts your attention to the song.  So, you either need somehting with little to no repetition - ala classical music - or something different, like trance.  I found that the non-existence of lyrics helped, as you didnt key in on what someone else was singing.  Additionally, the repetitive pattern was so short that it did not divert your attention, but rather caused you to get tunnel vision - it drowned out what was around you but made you hyperfocused on the task at hand. 

And on top of all of that?  Your typing speed goes up 10-fold with trance.  You don't even realize it but you type to the rhythm and can really fly.

This worked for me.  It's strange, but I tried testing the theory on some other friends as well.  It worked for some, not for others.  I would only use it as a last resort if you are really easily distracted by anything going on around you - use this to drown out what is around you.