a lot of the differences are more apparent to the player than the listener- you can "feel" them, more than hear them.
I couldn't agree more Dave. This has been my experience, and that of Joe Bonamassa!
To answer Hunter's question, this is the order I would place things in their importance to me. I've also grouped a couple as I treat them as one thing:
1. Amp
2. Speakers and cab (the combination of)
3. Guitar and pickups (the combination of)
4. Picks / strings / cable quality
It doesn't matter what the guitar is, I still sound like me. I can play Enter Sandman on a Tele and you'd tell it was me, and it wouldn't sound that different to me playing it on a PRS to most people. It would feel really odd though!!!