Clearly the rated voltage of the cap needs to exceed the actual max voltage it will face in the circuit. This ensures that its capacitance is nominally constant, and its lifetime is not degraded (i.e., it won't get damaged). It's best that the rating exceeds the actual voltage by a good margin (say ~50-100%), for best performance. And it's always wise to read the spec sheet of any electrical part, for more details and to educate yourself.
If a quality capacitor is being used within it's rated specs, then it should sound fine - i.e., like an ideal capacitor. Here, 'quality' includes things like small variation in value, low ESR, low variation with voltage, etc.