POM, PBT and ABS are all different kinds of plastic, and all feet different, and if you want to get really hyper-sensitive, they feel different on different switches. Also the thickness counts, and the profile. So there really is a lot to it. Each type of plastic has advantages and disadvantages. Here is my assessment:
PBT
It's the hardest plastic of the three, and you can feel it on your fingers, but it's also the most durable. It therefore lasts the longest before becoming shiny or discolored.
Printing can only be by dye sublimation or laser etched. Currently there is no known reliable method of making double-shot PBT's. Which means that all PBT keycaps must have darker legends than the rest of the keycaps. As such, black keycaps will always be otaku or near-otaku. Also due to the way PBT plastic cools in a mold, space bars are a huge problem to make. But PBT space bars are not impossible to make however, they just seem to be hard to make, and are probably expensive to make as well, so you don't see them very often. PBT is of course great for a gaming keyboard, since the WASD cluster will take a very long time to shine.
ABS
It's the softest and you can feel it on your fingers, but it's the least durable. It becomes shiny quite rapidly, and feels totally different when shiny. It also has a tendency to yellow, especially when exposed to UV light. But it can be made in double-shot injection molding process, meaning you can have any color legends with any color keycaps, including white on black. Many consider double shots to be the best looking keycaps. Not good for a gaming keyboard, because of the shine.
POM
The mysterious other. The least known, and the most over-looked. I have an awesome cherry profile set of POM keycaps. They are relatively thick. They feel great, especially on MX red switches. They feel smoother and "faster" somehow. However, I have only seen Laser etched and in-filled POM keycaps (and of course blanks). I do not think it is possible to double-shot them. Also I have never seen any dye sublimated POM keycaps, but theoretically it should be possible, if you had light colored POM keycaps to start with. I had a set of Chinese-made Rainbow POM jellies that felt great as well. But they were blank (which I didn't like at the time) so I sold them. But, I have a Noppoo Choc Mini with POM's and they don't feel as great as the Cherry-profile keycaps. And I'm not sure why.
As for the best?
I would say it depends on what you want them for, and what keyboard you are going to be using them on. And of course personal taste is the ultimate qualifier.
But I would say there are some opinions that are generally unanimous:
1. Thicker keycaps are always better than thinner, when comparing keycaps of the same plastic type.
2. Double shot ABS keycaps look the best, and come in a wider array of color combinations.
3. Dye sublimated PBT keycaps last the longest by far. I have a vintage Desko keyboard with a set of keycaps which contained a combination of ABS and PBT kecyaps. The ABS are worn smooth as glass, and the PBT have not even begun to shine. The Desko keyboard was obviously heavily used at an airport for years, but the PBT keycaps still look almost new. The ABS keycaps on the same keyboard are of course too shiny for words.
4. POM keycaps are used much less frequently than the other two. The reason? I have no idea.
