In order to understand why cables may sound different, we should look a bit deeper into theory.
In passive instruments, the serial impedance and inductance of the pickups, and the parallel capacitance of the cable make an RLC low pass filter. The main problem is not that much the cutoff at high frequency, but the fact that it is preceded by a sharp boost at the filters resonance frequency. It is this resonance frequency peak that is audible. All else being equal, the higher the capacitance the lower the resonant frequency. This is illustrated in the graph below:
View attachment 7311144
Here, I plotted the resonance frequency vs capacitance for a filter with impedance of 10 kOhm and inductance of 5.5 H. These are typical values for something like a P-pickup.
As you can see, for cable capacitance >200 pF, this resonant peak occurs well within the range of the bass harmonics, and it would be audible.
Good instrument cables typically have a capacitance <100 pF/m (about 30 pF/ft), with the best of them around 50-60 pF/m. However, even some expensive cables measure >100 pF/m. Imagine a 6m (20 ft) of one such cable, having a total capacitance of say, 700 pF. The resonant peak of the resulting RLC filter woud be about 2.6 kHz, i.e. somewhere in the high mid range. You'll get several dB boost around that frequency, followed by a rolloff above that frequency.
Now, if we take 3 m cable with a total capacitance of 150 pF (very good ones can really measure that low), we see that the resonant peak occurs above 5 kHz, where there is very little in terms of bass harmonics. Such cable, compared to the higher capacitance one from the first example will sound brighter and cleaner. There is more to it, such Q-factors, but I'll stop here.
Surely, there is more to instrument cables than just capacitance (noise rejection, flexibility...), but I hope this will help to clear the matter of instrument cable capacitance and sound even further.