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Ctesias' description is scattered in many versions all over the web. For convenience, I have pasted the least "contaminated" on his own page. The rest are pasted into Diodorus' page.
Having established that Herodotus had no reason to mention the gardens, we have removed the most obvious objection to Ctesias (that he appeared to be describing something that didn't exist). So now, we can look at Ctesias on his own merits.
Ctesias's History of Persia ("Persica") covered the whole period from the founding of Babylon to the current Achaemenid rulers, and thus started much earlier than Herodotus' Histories. Since Ctesias attributed the gardens to the founding queen of Babylon, he had good reason to discuss them, just as Herodotus had good reason to ignore them.
But Ctesias is still commonly dismissed as unreliable. As the Livius site makes clear, there are some surprising omissions from his history, including important names, battles and treaties. There is also a misnamed river, and he is accused of misidentifying an Egyptian traitor. All this tends to undermine our confidence in him—but the problem is us, not Ctesias.
Ctesias' description comes from his Persica (History of the Persians)—which does not survive. Much of it is known through later historians such as Diodorus where it is mixed in with other material, summarised, commented on and so forth, until we don't really know where Ctesias' work starts and stops. But the Persica was very fully summarized by Photius before it was lost, so we know what Ctesias had to say. We also know from Photius' comments that professional opinion at the time accused Ctesias of telling tall stories, and rewriting history.
Photius and his colleagues had the same problem as us: they assumed that history was about powerful men, battles, treaties and conquests. But Ctesias was looking at something else.
Photius' Summary (called the Bibliotheca, or Myrioblion, Ctesias is summarized at #72)—shows that Ctesias' interest is the women and eunuchs who caused, controlled, manipulated and derailed Persian history. His sources were the women and eunuchs themselves, and he includes only enough "normal" history to put their hair-raising activities into context.
So seeing Ctesias as unreliable is a trap. Ctesias' message for his reader is that we ignore "unmales" at our peril. In this light, Ctesias' Persica emerges as a rational work, and we can put reasonable confidence in his description of the Hanging Gardens.
Ctesias describes the gardens very coherently, giving extensive detail about the measurements as well as structural and mechanical information. In fact, it is these scientific aspects that seem to have interested him, and they are perfectly plausible in engineering terms.
Ctesias describes the waterproofing in considerable detail, discusses the hidden pump, and sets the whole thing on vaults (which are much more suitable than the columns mentioned by Clitarchus and his successors). As an account, therefore, it seems reasonably trustworthy.
Ctesias appears to be far more reliable as a historian than is generally thought, and his description of the gardens makes good sense. On the whole, I personally am inclined to trust him about the hanging gardes.