Actually, Gerard Edelman proposed a very elegant and plausible "explanation" of consciousness -- although, he would think of it more as an explanatory model of how consciousness is neurally possible. I won't go into it here, but if you feel like an interesting read, he's got two relatively recent books on the subject: "A Universe of Consciousness" and "Wider Than the Sky". Anyway, I agree with William that it is consciousness which provides the major difference. But then, if you read the Edleman book, you'll realize that my comment about human composers switching systems at the drop of a hat is, in fact, informed by Edleman's model of consciousness... (I cheated a little: I didn't give you the background for my comments! Nasty, isn't it! But I've been into the whole mind/brain theory thing for a number of years -- a hobby, of sorts.)
The whole subject of computers actually composing music, however, doesn't really interest me that much (nor really does the subejct of whether computers _can_ be conscious). But the idea of computers as something like automated composition assistants is, I think, very interesting. I even started messing around with this myself and have found that success depends entirely upon the creative imagination of the composer/programmer and also on her/his ability to quantify, in some way, what it is they find interesting in music. To simply tell a computer to help you compose music is, of course, a little silly. But to extract the essential, theoretical underpinnings of what you're looking for, and develop a representation of these in terms that a computer can work with can be quite rewarding. Now, before we all get into a battle about "creativity" and "robots" or whatever, keep in mind that I in no way imagine that the computer itself is composing, or even being creative. To me, the computer is simply doing what I ask it to do. It's just a slightly more abstract version of working with a sequencer -- the computer is helping. That's all. And there are many ways in which a computer assistant can be a very handy helper!
So it finally comes down to a knowledge and understanding of music. The computer is just a tool -- like a piano, violin, voice, etc. If you become good at "playing" it, then you can do some pretty exciting things. If not, then you'll never get beyond "Mary Had a Little Lamb". On the other hand, if I were a virtuoso pianist, I may likely avoid the computer altogether!
J.