I assume the best advantage to ceramic rims would be the ability to shed water easier due to their relative flatness. How much better are they? Does it make that much of a difference when breaking?
I don't think it's so much that they wick away water as that there's more friction to be had when wet. I haven't personally had ceramic rims before, but everything I've heard and read leads me to believe that folks who ride often in bad weather prefer them once they've tried them, due to easier braking.
I hope readers pardon the length of this answer, but it does raise some interesting questions about the performance of ceramic rim brake rims. This is not exactly an issue of cosmic importance. While there is reason to think that ceramic (or similarly coated) rims should reduce stopping distance, many riders don't routinely ride in the wet, experience can enable most riders to compensate for wet conditions, rim brake performance is good enough with good brake pads, and many performance bicycles are moving to disc brakes anyway.
Some of this answer draws on the work of Jobst Brandt, who was an engineer in the cycling and other industries, wrote a book on bicycle wheels, and participated actively in Internet forums and message boards. He appears to have been regarded very knowledgeable and/but very opinionated. Note that I'm not an engineer myself, so I'd welcome any corrections if the statements below are wrong.
What is ceramic and ceramic coating?
Ceramic materials actually have quite chemical compositions, and thus physical properties as well. Wikipedia defines them as brittle, hard materials made from "non-organic, often crystalline oxide, nitride, or carbide material." Relevant to cyclists, aluminum oxide (Al2 O3) is a ceramic material. In fact, exposed aluminum forms a thin layer of this material when exposed to air. And most of our rims are made from various aluminum alloys.
An ungated (and possibly pirated) PDF of the 3rd edition of Brandt's book, The Bicycle Wheel, is available here. I believe this was written in the late 1990s. In the chapter on rims (pg 53 et seq), he indeed describes this oxide layer as ceramic. Its thickness can be increased by anodizing. (Peripherally, you can also dye the anodized surface, and the oxide layer protects the dyes; however, the dyes can still fade with exposure to UV light from the sun).
Brandt described the ceramic rims of the time (remember, likely late 1990s and early 2000s) as having a thick ceramic coating on the braking surfaces, and he attributes the purpose as improving wet braking performance. Mavic appears to have been one of the pioneers of this process. One initial review and a later follow-up of their ceramic-coated Open Pro rims (NB: these rims were sold in a non-ceramic version as well) described the potential benefits. The reviews state that a) the hard coating was durable and it was thought to increase rim life, and b) the coating seemed to improve wet braking. This fits with my recollection of the advertised benefits as well.
More recently, some companies have started to advertise ceramic coated rims again. For example, Boyd Cycling advertises similar benefits to their ceramic coating as Mavic did. DT Swiss describes their coating process and its purported benefits here. Mavic themselves now offer some rims with an Exalith coating, which is similar. November Bicycles, which specializes in custom wheels, cautions that all these coatings are actually PEO, or plasma electrolytic oxidation, which November maintains is not ceramic. PEO is an electrochemical surface treatment process that generates oxide coatings on metals like aluminum.
Hence, I suspect that older style ceramic coatings and more current PEO coatings may both be processes that create thick aluminum oxide layers on the rim - thicker than you would normally see in regular rim manufacture.
What causes braking performance?
Brakes create friction between the brake pads and the rims. In the wet, a thin film of water collects on the surface of the rim.
Brandt argued that wet braking performance was primarily affected by how rough the rim surface was (pg 58). And indeed, he describes ceramic surfaces (at least the type used on rims) as rough, not smooth as the original question said. Brandt says that at a microscopic level, aluminum is inherently rough. In fact, it's rougher than steel. He argues that a rough surface penetrates the surface film of water better than a smooth one. He did not explain, but I would assume that there's a chance that because a rough surface has higher peaks than a smooth one, those peaks should catch on the brake pads and create friction earlier than a smooth surface would.
Secondarily, the brake pads mechanically displace the water film. Brandt argued that smooth surfaces should have thinner films of water. And while this may be counterintuitive, he thought that because water molecules closer to the surface of the rim are more solidly attached to it, thinner water films were harder for brake pads to displace.
This offers some rationale for why ceramic or PEO coatings might improve wet braking performance. I don't believe that wicking water away from the rim is the issue. One unanswered question is this: manufacturers might be able to make some PEO coatings hydrophobic (NB: they can be applied to a bunch of materials, not just aluminum, and they may not have uniform properties even on aluminum). I've found no mention of hydrophobic properties in any of the advertisements for bike rims. It seems like this might provide an advantage in wet braking, provided you could maintain the other material properties of the coating. If nobody has advertised this, then I assume it might not be possible or cost-effective to apply, or that it ruins other properties related to braking.
Interestingly, Brandt thought that ceramic coatings were of no advantage in dry conditions. He also argued that because the oxide layer is a good insulator, it raises the risk that your brake pads would overheat, thus compromising performance. With a thinner oxide layer, braking heat should more quickly transfer to the rim and dissipate (aluminum conducts heat very well). This argument is developed in more detail on this archived rec.bicycles.tech thread. This has not been my personal experience with Boyd's PEO coated rims, which I'd expect to have similar physical properties to the ceramic rims of his time.
Objectively answering the original question
In principle, I'm sure someone could set up a test rig to try out a ceramic/PEO rim versus an equivalent non-ceramic/PEO rim. So far, my search has not found an experimental trial. You are thus left with user perception. For better or worse, user perception is vulnerable to placebo effects.
Nevertheless, collecting a wide spread of user feedback might be the quickest way to get some answers. Surprisingly, feedback is mixed. For example, this thread on Slowtwitch has two people saying braking was better, one saying no difference, and one person seemingly saying that in the wet, the rims appeared not to brake at all for a couple of seconds. A couple of people on this Velocipede Salon thread seem to corroborate the latter assertion, although others there said positive things.
I would expect manufacturers to have done lab tests on this subject. I am not aware of any independent lab tests. In fact, manufacturers don't seem to make their testing results on this subject available. However, this post on Velocipede Salon was made by someone claiming to be a Mavic community manager, who said:
The ceramic rims performed only marginally better in the lab compared to standard aluminum, although they did reduce brake track wear quite significantly. On both points, the Exalith performs much better than the ceramic rims did ... Exalith is meant to pick up where ceramic rims left off. The braking is outstanding, in fact better than the ceramic rims. Stopping distances (wet and dry) can be measured and confidently stated to be reduced by almost 20%, according to Mavic engineers.
(NB: Here, the writer uses ceramic to mean Mavic’s older style ceramic coatings offered in the late 1990s and 2000s, and Exalith to refer to a more modern PEO coating that’s probably similar to what Boyd and DT Swiss use.)
I've had Mavic rims with Ceramic braking surfaces - They are brilliant, far better braking power - especially when wet and they last forever.
I'm unsure why they work better in the wet - but they are significantly better in the wet and the dry too.
Thoroughly recommended. Shame they stopped doing them.