I know I am 5 years late to the question, but I'd like to offer an answer from a more objective point of view, since I think the question will remain relevant as long as these 2 kinds exists. (Perhaps the author of the question doesn't even care about this matter anymore, but like me, there's new people joining every day so my answer is mostly aimed to them.)
The question was "Clay VS Ceramic: What makes one which better than the other?"
I want to, very respectfully, point out that most of the answers here actually answer a different question: "Which one do you like best?"
Don't take me wrong: I do think those answers are valuable and offer much perspective; from a very subjective point of view.
I've also seen some objective answers here, so I'm not even being original. (Just trying to be more comprehensive.)
I, too, think (as it was also stated here before) there's room in our world for both; but I'll go further and point out that one thing can objectively be better and yet, there will still be people who'll reject it, simply because they just like more the other one.
By leaving subjective parameters aside, we could get an objective answer:
Cost efficiency: Ceramics are better.
Ceramics are less expensive. The higher the quality, the more the gap widens. In general, to get Clays at a similar price as Ceramics, some quality will be lost.
Weight: Clays are beter.
Chip weights preference is subjective, but how much a chip can weight is not:
Currently, (I'd love to be wrong) the only way to control weight for Ceramics, is changing their size (or volume, like its thickness, for instance).
Clays can be slugged or not, have different ratios for its composite formula components, or even be weighted with brass flakes.
So Clay chips can have, at the same size, a wider range of weights.
Fragility: Ceramics are better.
I've seen Clays being snapped (way more difficult if metal slugged, true); some can be easily broken just by hand, while others will require a hammer blow.
But you'll need to do something like putting ceramic chips in a blender to be able to make a dent or two (before they break the blender).
Sound: Clays are better.
How a chip sounds is completely subjetive, but how it can sound is not:
Ceramics of the same size, pretty much sound the same.
Clays simply have a wider range of sound to them, to choose from.
Design flexibility: Ceramics are better.
Yes, designs are inherently subjective, but there's a way to evaluate this objectively…
Nowadays (especially if you request them to be aligned) you can make a ceramic chip look like a clay chip. You can't make a Clay chip look like the elaborate designs a ceramic chip can have.
The flexibility ceramics offer, to pretty much portray any design imaginable, objectively surpasses that of Clays.
Debossing: Clays are better.
Maybe I'm just missing something, but it seems to me Ceramics are just always flat; while Clays, rarely.
Clays can have, not just patterns, but even words debossed on them.
(Ceramics can have writing too, as part of their design flexibility. You can have printed text, even on the edges, yes, but I have never seen debossed text on them.)
Smell: Ceramics are better.
Yes, some chip smell, and if it does, you can bet it's not a ceramic chip. If the smell was good at least some times, this would be a subjective matter. But it's always bad (and maybe even toxic) which makes it binary: No smell is better.
Stackability: Ceramics are better.
Of course someone can say: "I don't like flat chips", but it's a simple objective truth that flatter chips stack better. The best Clays are flatter, yes, but even then not as flat as Ceramics.
Durability: Ceramics are better.
I've seen reports of Clays falling apart, crumbling (after many years, yes). Maybe something similar can happen to Ceramics, but I haven't seen it.
(I've read that ceramics' designs can fade, but it's supposed to happen only with heavy casino use.)
Spinners: Ceramics are better.
I've read people listing Spinners as being more common among Ceramics. I don't see how (but I am open to changing my mind).
As I understand it, spinners are a result of imperfections on the chips surface, some protuberance. Ceramics are very flat and the injection point is always (nowadays at least) on the side. I just don't see how could there be more spinners among Ceramics than in Clays.
Maybe I've left out enough (objective) parameters, where Clays are better, to conclude they are the better option. If that's the case, it was not intentional and I would gladly amend my list. As it stands, it is obvious to me that Clays are, objectively, better.
But!
What about subjective parameters?
Timbre, tactility, collecting value (like Paulsons, for example), nostalgia; to name a few, might even be more important for some, and I think that's just fine.
I am not trying to say that everybody should prefer Ceramics. I just think there are chip aspects that can be evaluated independently of personal preferences.
(I am still undecided myself, and also still awaiting for some more samples to arrive.)