I'm one of those 'fools' that believe everything makes a difference. That is true for everything, and also guitar amps. Whether that difference can be heard, when inserted between a hundred other differences, is the real question.
First of all, I believe that whenever dealing with a components where the rating far exceeds the application, say a 400V capacitor in a guitar, the difference is near non-existent. If however, one were to use the same capacitor as a coupling cap between the phase inverter and the ouput tubes of a big marshall amp, those differences may be more apparent.
A capacitor is basically an insulator with polarizing properties, sandwiched between two conducting sheets. as Q = C*U, the charge stored in the capacitor is a product of the capacitor size and the voltage. The amount of charge is mainly limited by the electric field / voltage, breaking down the dielectric material as it becomes a conductor instead of an insulator. As Ic = C*dv/dt, the capacitor current, and hence the magnetic and electrical fields progating through the capacitor, is determined by how big of a surface area you have for the collection of charges on either side of the dielectric, and how fast you are able to remove or capture those charges (dv/dt). The quickness of the charges, is mainly a factor of the dielectric polerization properties, that is how fast you reorinate the dipoles inside the insulator.
Now say you leave this charged non-ideal capacitor out on the table for a very long time. At some point before the end of days, the charges will eventually migrate across the dielectric material, until the voltage of the capacitor drops to zero. Even with the best insulator materials, small leakage currents will exist in a capacitor, and can be modeled as a parallel resistance across the capacitor.
More over, when the electric field is nearing the dielectric field strength, generally that is, when the voltage across the capacitor is close to its voltage rating, interesting things can happen. Effects like corona, where a high enough voltage will cause nitrous and ozone gasses within voids and imperfections of the dielectric to become ionized, can account for much of the capacitor degredation over time.
So.. with all these things in mind, one should consider the right capacitor for the right application. Do you have current variations that are high and fast, like in some switchmode converters? You may want to use polyester caps with low ESR rating rather than electrolytic, to avoid excessive power dissipation. Do you need an op-amp with a high bandwidth? - that dv/dt aka slew rate, will play a major role. Do you want those ultra high frequencies to get through your capacitor? You better make sure your dipole reorientation is fast enough (99.99% of the time it is, don't worry).
In any case, it all goes to show, that if you take two capacitors with the same ratings, variations between each individual capacitor, to variations between design, manufacturing methods, material properties and even variations between the surrounding due to shape and size, will probably have some impact on the signal. How big that impact is however, is completely a case by case study.
Kind regards
Christian