While gelcoat is typically gelcoat (profound, I know
), paint can mean a wide variety of coatings. So it's hard to compare in general terms.
Getting a bit more specific, there are a number of two-part paints (really they are more "coatings" than paints) that are very durable and will keep their shine for a decade or more (my boat had been painted with Awlgrip and was still shiny 25 years later, however it was not in a sun-baked climate; but, neither was it stored indoors).
A number of high-end boat manufacturers are now painting
their boats straight from the builder with two-part LPUs (polyester-based polyurethane), such as Awlgrip and Alexseal, and skipping the gelcoat altogether.
One potential downside to this type of coating is that it is a bit trickier to repair than gelcoat; however, the overall look is usually so good that I find a few nicks are fairly "invisible" if you are not looking for them. And it can be repaired, just not quite as simply. It forms a thin "shell" on the surface of the coating, and this is part of why it is so hard and shiny, but also why it is more difficult to repair and somewhat more vulnerable to chafe. This also means you cannot buff it out (until it is very old and you have really thrown in the towel and are just prolonging it a bit).
There are also coatings such as Imron and Awlcraft 2000, (acrylic-based polyurethane). These are somewhat "softer" than the LPUs and can be buffed and repaired more easily. On the other hand, you could say that the Awlgrip type coatings don't need the buffing or repairing (as often). I'm not sure there's a "for sure better" choice there, but more a case of matching the coating to your bent and your situation.
The one-part paints are easier and less toxic to apply, and also less expensive, but they are not as durable and the shine, especially, will not last as long. But again, these have their place in the grand scheme of things. An example of this type of paint would be Interlux Brightsides. They make reference to "polyurethane" in the name, but it is basically a modified alkyd paint, and not the same as a two-part LPU (polyurethane).
And then there are the other types of paints and coatings that I'm not as familiar with, so you can see how it's hard to easily cover "gelcoat vs. paint."
If I were to paint my egg, it would be with a two-part coating. Since the prep is the main bulk of the work, I would want the long-lasting qualities of the two-part coating.
PS: As a side note, do check the care recommendations for your specific coating, if you do paint. Awlgrip, for example, does not recommend waxing over their product. (They do, however, sell a special polymer that one can use in place of wax, if one wants to.)