Great idea for a thread!!
I think every little thing adds up to a difference... walk into a big chain guitar store, grab all the guitars they have of a same model (Fender AmStd Strats or Teles work well for this as stores normally have 5 or so in stock) and plug them all in one after the other without changing the amp settings... it's crazy how different they can sound! Sometimes it just comes down to all those pieces coming together perfectly, on one particular guitar, and then some magic happens and that guitar will have mojo none of its brothers do.
In regards to different models from different brands made in the same style (all the various strat copies out there for example), it's most likely to be the electronics, even something as small as the quality & brand of pots & caps used can make a huge difference to your tone, the type of woods & quality can affect the tone, the quality of metal in the hardware (tuners, bridge) will affect the tone, and some will even argue that the thickness & type of finish used will effect the tone to an extent.
I really think every guitar on the planet has it's own unique personality, and will bring that to its tone.
But ULTIMATELY the biggest thing to affect the tone of a guitar is the person playing it. You can hand Segovia a beginners firewood-grade guitar that you think sounds terrible, and when he plays it, it will sound like Segovia.