The following does NOT apply to electrolytic caps.....
The frequency it operates at will dictate the choice of dielectric material used. We commonly see paper & oil, and plastics like mylar and polystyrene used below 30 kHz.
Mica and certain ceramics still rule supreme at RF, tho teflon is making some inroads.
The choice of dielectric material in a cap will have a direct effect on it's power factor, which is strictly an AC proposition. That in turn will dictate the ability to handle the relationship between current and voltage impressed upon it. It is easy to see the result of exceeding ratings.
Caps used on DC (that is without any AC ripple included) rely only on breakdown voltage across the dielectric. AC ratings are usually lower than DC ratings for any given cap.
A uF is a uF in ratings terms. Doesn't change unless it is obviously a variable capacitor. The manufacturers tolerance rating also comes into play, but usually that is a not a point of order.
Excessively high operating temps also will cause a good cap to fail. To wit, I have a big paper-n-oil cap that has a water cooling pipe wound thru it. How much larger would it be if dry?
What matters is the use category as stated above.