Cap value and tone?

Aside from the more obvious change, (when you turn down the tone
control, bigger caps cut more highs and volume) even without turning
down the control, the tone cap can affect the sound slightly.
That why PRS eventually added a switch and dummy tone control circuit to their early guitars.
Without a tone control at all, the sound is slightly brighter and
edgy, with less midrange.
Higher value caps shift the resonant frequency of the pickups and wiring
combination to a lower frequency and allow a slightly warmer/fatter
tone. This modest effect is perhaps more noticeable to the player than
a listener and varies in intensity with different pickup and pot
combinations. Strats are perhaps the most sensitive, and metal covered
humbuckers probably the least sensitive to these changes.
It's probabaly best to use a switch to try out different caps while
you're playing, to really be sure how much difference it makes, and to
avoid voodoo and/or wishful thinking..

What's often lost in the discussion about tone caps is
that they're NOT akin to the coupling caps in a guitar amp or tube
Hi-Fi amp. Those caps are conducting the signal (your tone) from one
stage to the next and decent grade caps are usually more efficient at
higher frequencies, and sound 'better'. You CAN actually hear a
difference, although many amps including Fender and Boogie, intentionally use a low-grade ceramic cap to couple the pre-amp to the power-amp. It's a slighty darker, grittier tone.

But all this vibe about using high-grade caps is pretty meaningless in a
guitar tone control. The cap isn't conducting your tone at all, it's
merely rolling off some treble to ground...sort of a detour.
With that in mind, it's arguable that a LOW-GRADE cap would be
better for a tone control. More inductance and a poor high-frequency
characteristic would leave a slighty clearer tone, if anything, and
reduce the effect of the tone control when it's fully dimmed-out....and
they certainly seem to be pretty common. If Fender, or anybody else,
could noticeably 'improve' their guitar's tone by merely susbstituting
a cap costing 50 cents more, they'd have figured that out a long time
ago.