Thanks for the question.
The answer in detail to this question is very long, and at some point its worth a detailed answer, as there are quite a few interesting issues to consider. But this is probably not the place for that long discussion, so I will try to be brief. I'm happy to provide a more fulsome answer should anyone want/require it.
The CC BY is a copyright based licence (ie. it's enforcable by the copyright holder / licensor because copyright subsists in the material to which it is applied). It rely's on copyright being maintained in the material. I use the word 'maintained' carefully because copyright does not last forever. When it expires, the material licensed under the CC BY will become "public domain" (in the copyright sense, not as in "accessible by the public", though CC BY material is likely accessible to the public anyway) material. Copyright has gone, and the licence falls away as it ceases to be enforceable by the (now former) copyright holder.
The CC0 is not generally considered a licence at all (though, in some situations it might behave like a licence), rather, its referred to as a waiver. That's because its intended to operate to extinguish copyright protection immediately and before it would otherwise expire. A copyright holder applying a CC0 does so because they wish to abandon their copyright ownership over the material to which it is applied.
There are some issues that flow from the use of the CC0 that relate to both its construction and application. The first is that some lawyers do not consider that you can, at law, abandon your copyright, or at least, in some countries, copyright law either does not permit it, or is silent, giving rise to uncertainty. You may, of course, choose to abandon any enforcement of your copyright, but abandoning your copyright is quite another thing. In my humble opinion, I think you probably can abandon your copyright in Australia.
The second issue concerns lesser known "moral rights". Moral rights are the rights of an author (whom may or may not be the copyright owner) to be attributed as the author of their work, to not be falsely attributed, and to prevent derogatory treatment of their work. Australia recognises moral rights in the Copyright Act, though they are not copyrights. They are not economic rights. They cannot be sold or licensed as copyright can be. A similar question arises with moral rights - can you, as an author abandon your moral rights under the CC0?
The CC0 operates to the extent that applicable law allows. Consequently, "certainty" emerges as an issue. And you want to provide certainty, right? Thats the point of a licence (or waiver)! You use it because it provides certainty. Well, in some cases, the CC0 is less than certain.
The other aspect to this is the limitation of liability clause in the CC0. It carries some weaknesses when compared to the quite robust and thorough limitation liability clauses of the CC licences. I have discussed this matter with Creative Commons HQ with a view to modifying the CC0 limitation clauses so that they are inline with the CC licences, nowever we are not quite there yet.
In terms of implementation, the CC0, while theoretically useful, is not something that some organisations find palatable. Some institutional/government data providers DO NOT want to abandon their copyright. They WANT to be attributed. So the CC BY, for them, is a better solution.
There are criticisms about CC BY that lead people to consider the CC0. Attribution stacking is one such example. But in my respectful opinion, those problems can be easily dealt with, or are not problems at all. Indeed, when you look at the text of the CC0 waiver, if it cannot operate to extinguish copyright and moral rights fully, it falls back to being something like a CC-BY without an attribution requirement. So, if your decision is between the CC0 or the CC BY, why not apply a CC BY, anyway? Its got a better limitation of liability clause, and as the licensor, you can tell users that you do not wish to be attributed! (attribution=null)
I note that this question has come from the research ODI Deep Dive session. Readers may be interested to note the recent publication of the RDA & CODATA Legal Interoperability Of Research Data: Principles And Implementation Guidelines. I talk about some of these considerations in Guideline 1C.
Is the CC0 more appropriate for open data? Theoretically, it probably provides a more 'pure' openness. Public domain material is THE most open material you can get. But unfortunately, what the law giveth, it also taketh away, due to international inconsistency and differing interpretation. On the other hand, while not as open, the CC BY licence probably provides better certainty of interpretation, with very few side affects once you consider the flexibility of what licensors can do with the CC BY. Slapping a CC BY licence on a dataset is the most common, and simplest implementation of CC BY, but as a licensor you can be more creative than that with a CC licence, if you like.
Happy to discuss.