Every guitar I've ever owned sounds different. I have three strats. They all sound like Strats, but each one sounds identifiably different. I have owned a mess of Teles. Again each one sounds different. Same for amps. I think its just a question of what you are after. I made my mind up to get a sound that was unique to me and I went through amps, guitars and effects until I found the gear that came closest to what I had in mind. Its just so personal. Its a combination of technique and the right gear--for you. We might sound like crap if we played on each others rigs--then again--maybe not!
I settled on a 70 maple neck Telecaster with Joe Bardens. That goes through a Dynacomp, A fulldrive, Tubescreamer, Rat, Dan-Echo, Micro amp (not all on at once!) My amp is an Allen Old Flame. I can get a wide variety of tones with all this stuff. From fat and jazzy to mondo distortion to rip your face off blues.
I have this theory that the lighter your touch, the less the personality of a guitar seems to matter. I think a hard attack really brings out the differences. Thus, a player like Eric Johnson can play a Strat or a 335 and sound almost the same on either. Play hard and the transients jump out of a Strat or Tele.
I'm probably not even answering your question, but maybe part of the answer is in there somewhere.