Hi Hoeycow: I think it's a very good question, and I think there doesn't have to be just one answer.

Replicating note for note is an excellent discipline when we are learning. It means you can't avoid bits you find difficult so you have to master passagework you might otherwise skip past. And it is good training for the ears too: sometimes it is hard to pick out what someone is doing, and listening again and again teaches you to pay close attention to sounds you otherwise sometimes only hear as a blur of notes.

On the other hand, if we are going to perform music to others then it seems nice to bring something of ourselves to it, rather than just deliver a facsimile of someone else's playing. In that case there are no rules: we can just alter a bit of phrasing or we can change the whole feel of a number. Some of my favorite tracks are where someone has taken a slow song and done it fast (or vice versa), or a highly orchestrated number and pared it down to the bare bones (or vice versa), or a happy song and made it sad (or...).

Still. If we're going to add our own ideas to a number - we'd better have some good ideas. That's the tricky bit.

Cheers - C