There are few generalizations with respect to capacitance at voltage.
The best, but still weak, is physical size. A large cap is more likely to be filled with electrodes, and so a smaller value (say 10nF) will have them spaced more widely and bear a higher voltage cutoff*, and a larger value (say 10uF) will be low.
*The voltage where capacitance drops by, say, 30%.
Certainly, a very large value, at voltage, needs a large volume. There must be some physical limit to energy density. Of course, there's nothing stopping them from putting like two electrodes inside a tall ass 1210 and calling it a "0.1uF 50V" when it runs out of piss at a mere 10V.
I have seen little correlation between rated voltage, and voltage cutoff. I've seen parts by Taiyo Yuden and others that are 90% gone at rated voltage and cutoff at say 20% of the rating. I've seen Samsung and Murata parts which are rated for 6.3V but are still going at 10V (though the published curves rarely extend beyond rated voltage, YMMV).
You'll also often see families of parts, where it seems to be the absolutely identical component, just bearing different voltage ratings. Presumably you are paying a little premium for quality -- hopefully, they were tested to that voltage, but yeah as far as I know they may very well be utterly identical parts. No difference in C(V), obviously -- might as well get the cheaper (lower voltage) option that still suits the application (C at V and V rated >= V needed).
KEMET gives curves but I find them dubious as they're all the same copy-pasted piecewise curve -- someone did shitty analysis there, but they still stick with it. Maybe the data are representative, I'm not sure. AVX is a big name but does not publish curves. No design-in from me. Most Vishay brands, same thing. Samsung seems to be hit and miss: maybe 50% of their parts link to a characteristic sheet, maybe 50% of those have a link
that doesn't 404, and maybe 25-50% of those have a curve that is acceptable for my application. TDK you have to download SEAT. KEMET and Murata have their databases accessible online.
The only solution is digging through lots of datasheets, and often not datasheets but char sheets, web tools, and downloadable databases. It's tedious, selecting one capacitor takes tens of minutes.
A final note about type: don't be tempted by high density types: Z5U, Y5P, even X5R is on the marginal side. All of them age terribly (C drops with log(time since soldering)) and have steep C(V) or C(T) curves. X7R is the least objectionable, or numbers nearby like X8R and such (look up
ceramic capacitor codes) also perform well, and are just produced less.
If you don't need large values, or can afford a pricey cap, and do need high stability, C0G is essentially an ideal capacitor formulation! They also outperform [non-electret*] type II dielectrics at high voltages (100s V), worthy for dense energy storage.
*There's a technology where the type II dielectric is poled either by applying voltage and temperature during manufacture, or in use (I don't understand how spontaneous poling works, but apparently it's a thing??). Cera-Link is an example brand. By building in a trapped electric field, the high-C characteristic of the dielectric can be shifted towards a usefully high voltage, e.g. centered on 300V or so. This
massively increases the energy storage!
Good luck,
Tim