The notes matter the most; the tone just allows the notes to fit in and be heard in the mix. If I don't like what I hear, the first thing I check is the notes I'm playing, then my technique. Nine times out of ten, it's one of those things.
The best players I've ever encountered spend approximately zero time obsessing over the nuances of string selection, pickup upgrades, tone wood, pedals, eq, amp settings, etc., and sound like themselves on any instrument they pick up, through any rig.
That's a long way of saying... tone is in the fingers. You can try to cover up bad technique with electronics, but if what you're playing isn't musical or doesn't fit the piece or isn't executed well, no amount of "tone" is gonna help ya.