I have kydex and leather holsters and each have their advantages and disadvantages. All of my holsters are for a 1911 pistol with a blued slide so my experiences may be different than somebody with a different pistol.
I like that kydex doesn't require much, if any, break-in. A well made leather holster is often so tight it may take several days of break-in to get a reasonable draw. Most kydex holsters come with tension adjustments to allow you to adjust the tension to your liking. The tension of just about any kydex holster is plenty for concealed carry purposes.
I like that a pistol positively snaps in to a kydex holster when you holster the weapon. With leather, especially when new, you are often pushing and then pushing some more to get the pistol properly seated in the holster. With a 1911 you can engage the thumb safety and jam the pistol in a tight, new, holster. I've often wondered if when holstering a Glock (or similar weapon) in a new tight fitting leather holster, with their square slide, light recoil springs, and no slide lock, if you end up cycling the action if you don't block the slide some how.
Usually, you can get a custom kydex holster much quicker than a custom leather holster. Most, though not all, of the top leather holsters have delivery times measured in months rather than weeks and often days as is the case with custom kydex.
Kydex is also impervious to wet weather and sweat. If you sweat a lot, it may take more than overnight, to dry off your leather IWB holster. It isn't a problem with kydex.
On the down side, an unlined kydex holster can be very rough on the finish of a pistol. A Glock may never show any wear from a kydex holster, but the beautiful blue slide of my 1911 showed long scrapes through the blueing along the top of the slide after just a few presentations from a kydex holster. Leather will also wear on the finish, but it is a little more subtle and will occur over a longer period of time.
Most OWB kydex holsters do not conceal as well as most leather holsters. I''m sure that is because kydex has usually been geared towards competition due to the greater speed of the draw from kydex. With the advent of the Raven Concealment Phantom, and the various knockoffs, kydex has become more concealable, but I still think leather holsters have an advantage in concealability. Leather is also a little more comfortable, to me at least. There is also something to the smell of leather and the beautiful craftsmanship of a nice leather holster.
In general, I like kydex, but leather seems like a better match for for my 1911. If I carried a Glock, or similar pistol, I'd probably go with kydex. They are light weight, weather resistant, inexpensive, and easy to get.
I have no experience with nylon, and can't think of any advantage for a nylon holster other than cost.
Here is an article from Duane Thomas called "The Case for Kydex"
https://www.usconcealedcarry.com/ccm-columns/features/the-case-for-kydex/
Here is holster maker High Noon Holster's take on cow hide vs horse hide. I have no experience with horse hide.
http://www.highnoonholsters.com/_Questions/_questions.html#1
The High Noon Questions section is one of the best in the industry. Whether you like their holsters or not, they have a bunch of good holster construction and design information.
