The pick ups will be the most significant impact on the sound of any given guitar. Other things will impact, of course, such as the large surface of metal that makes up a Telecaster bridge is responsible for the inherent twang (I realize you are playing a Schecter, this is just an example). Wood, combinations of wood, frets ...all the little bits and parts all together combine to create the unique sound of a particular guitar.

You could try different strings, say .09's and see if you lose the twang or not. But I do not believe strings have quite the impact other people do. Certainly not enough to redefine the characteristics of a guitar. Just imo of course! :)