The guitar amp's preamp has the biggest affect on the tone. Period.
Everything else "shapes" or "tweaks" or "enhances" the tone.
A fender twin sounds more or less like a twin regardless if it's played with a Les Paul or Strat or an ESP with EMG's, whether it's played through a vintage 1x12 or a krank 4x12, or mic'd with a 57 or a neumann.
It will still sounds miles apart from an Uberschall on the lead channel with the gain cranked.
Now if you said what is more important in getting a good tone, then I can see arguments for pickups, cabs, mics, etc.
But the poll was (roughly) which component has the biggest influence on the end result? Thus, the guitar preamp is the obvious choice.