It depends on the tone.
And no, that isnt a cop out.
Some tones (SRV, EJ, Hendrix) are hands dependent.
Some (modern metal) are more speaker dependent.
Some are amp dependent. Try and sound like Schaffer without a Larry or peak Metallica without a boogie.
Some (OSDM/HM2) are more pedal dependent.
Some are guitar dependent. Try and get a setzer or RBF tone without a gretsch.
It seriously all depends on the style and the tone you're going for. You're going to have to have a good performance either way, but I consider that a prerequisite to everything.