The value of the capacitor determines how much treble/brightness will be rolled off by the tone control.
The higher the cap value, the darker the tone will get when the tone control is turned down. The cap on old Strats and Teles was 0.1mF (so they could get really muddy), later ones had 0.047mF, most new guitars use 0.022mF as standard.
When the tone control is on 10, the value of the capacitor has very little effect, but it does have some effect as the cap is still part of the circuit.
The construction of the cap also has an effect. You can get anything from ceramic caps which cost a few pence, to polypropylene Sprague Orange Drops, to Hovlands which are about 10-15 quid each, to vintage paper-in-oil caps which cost a fortune.
It's worth experimenting with different values of caps, but try the cheap ones before shelling out big bucks!