Not saying that an unsaved person can't overcome things... but they don't have that same power as someone with the Holy Ghost within to overcome things.
That's the fundamental difference. We have the birth of a new nature.
This new nature, which is born in the image of God, now contends with the old nature which opposes God. Paul speaks of this contentious war in the book of Romans, especially in Chapter 7.
That's why the, "all things being permissable, but not expedient" quote mentioned above can be used on both sides of this discussion.
We have the power avaliable to us, but decisions and choices can inhibit us from seeing the benefits of having that power, displayed in our lives.
*** I want to re-iterate that I don't intend to say that a believer who plays, listens to secular music, is not saved. I am saying that I believe it is a hinderance to the growth process, as are many other things ***