When designing a board, it depends on what your designing.
If your designing a filter network, you have to take in account the rate of charge, and whats known as the "reactance" of X sub C. This is basically the resistance(impedance) of the capacitor over a span of frequencies. Known as the ESR in a way.
So for example, when building a low pass filter, you want a shut to ground at high frequencies. But the roll-off point is calculated in a Resistor-Capacitor filter from an RC formula, there are multiple other formulas for other filters. You have to damn near be a mathematician to engineer electronic circuits. Me, Im not but i have enough experience to know exactly what to do and how to handle it.
Anyway, In SMPS circuitry most of the output is basically whats called a Pi-Filter. The formulas that calculate the proper values of components are all over google, but basically its purpose is to knock out noise over a given frequency or range of frequencies. And how this works is by varying the total reactance (impedance) of the circuit over a frequency spread. This is all calculated out via a set of formulas. Basically in a nutshell components values are always figured out by using math depending on the circuit.
Most pi-filters are based upon 2 caps and an inductor in-between. For example if you design an SMPS with a fundamental frequency of 80Khz, you would want your pi-filter having a reactive value of nearly 0 ohms to ground at that particular frequency. so the switching noises dont make it into the load. This is why ESR is important, as you want as close as 0 ohms as possible at the given frequency.
If its >0 heat goes up inside the capacitor and will cause it to vent/leak. The rate this occurs is in another formula.
So in a nutshell, the filter cap values are important, But there is some wiggle room. But careful, you do NOT want to exceed its original uF value grossly, or it can de-tune the pi-filter enough so switching noise will get through. Some better power supply designs compensate using high frequency ceramics to make sure any electrolytic drift wont affect the output too much.
But at the same time, Capacitors especially electrolytics are cheaper and more commonly available in its regular values. so when engineers design the circuit, they usually use precision resistors/inductors which are available in nearly any value, to compensate for the roughness in the electrolytics. this is what gives you the "leniency". Also voltage can get important in critical circuits, it is very very small, but voltage does change the charge curve a little bit. But again, this is small and in a less critical application such as an SMPS, its almost non-existent to even matter. So i could stick a 1500v cap in place of a 15v and it isnt going to matter.
I could go on and on and on. But this is basics in a nutshell. In SMPS or analog environments you can get away with even the most basic of formulas without much trouble. However, in RF circuits all this stuff becomes highly critical and tolerances have to be tight. Heck, even routing a trace 45degrees to the right instead of 38.5 degrees to the right can make or break an entire RF stage. Yes, it can get that critical. Just saying.
Here is a link that pretty much mathematically explains capacitors:
http://en.wikipedia.org/wiki/Capacitance