The topic of Wikipedia contribution has come up before, but I am interested in the community's opinion on peer-reviewed wiki publishing (e.g., Scholarpedia). I would like to know if there is any advantage for a PhD student to publish in such an online venue versus the traditional journal publication for review content. The advantages I see to the wiki approach is free of charge publication, open access for all, not necessarily being limited by character limits. However, the disadvantages I see could be the citation being completely ignored by the intended audience and therefore missing out on the benefits of scientific communication and the possible loss of accompanying reputation for the publication. I would also worry these publications would be ignored or minimized by future supervisors and review committees.
Scholarpedia has adapted many of the processes of a peer-reviewed journal. However, it is still a kind of encyclopedia and not a research journal at all. Note that I'm not making any kind of judgment or evaluation in the previous sentence: the main page of the site reads
Welcome to Scholarpedia, the peer-reviewed open-access encyclopedia, where knowledge is curated by communities of experts.
So you seem to be asking: "Should I publish my paper in an encyclopedia rather than a research journal?" I think that's a kind of strange question: have you really written something which lies ambiguously between a research paper and an encyclopedia article?
The above is not a rhetorical question: please let us know!
It is also possible that I have fixated too much on "scholarpedia" and it is not the type wiki publication that you really intended. If so, please let us know. It would be helpful to give at least one specific example of the kind of "peer-reviewed wiki" you have in mind as a plausible alternative to a research journal.
Added: @MHH has helpfully clarified that the OP is probably talking about a review paper, or what in my field would be called a "survey paper". (The word "review" was also used at least twice in a different sense in the OP's question, and that was enough to confuse me.) I must begin by admitting that review/survey papers are rare in my field (mathematics), and that they would be written by PhD students is almost unprecedented. So I am almost at the point of wanting to delete my answer for lack of understanding and relevant expertise.
However, let me first try this: it seems to me that a review paper should be published in a research journal if it contains original research: i.e., some kind of synthesis, analysis, new perspectives, helpful simplifications, and so forth are being added. Of course "original research" is exactly what is not wanted in an encyclopedia article, although I don't see why this would necessarily be the case for all peer-reviewed wikis. So going more from general academic common sense than specific insight (i.e., caveat emptor), I would say that this should be the deciding factor between publishing a survey paper in a research journal or in a wiki. Let me further say that most or all of the advantages cited by publication in a wiki can be achieved by publishing in certain kinds of research journals: "free of charge publication, open access for all" certainly. Many electronic journals do not advertise hard "character limits", but of course there must be some kind of upper bound must exist, right? No one wants a 5000 page survey of the literature.
I think there is no definite answer at the moment since one can not judge now how scholarpedia will develop. At the present stage I think that the impact will be low and many colleagues may not know about scholarpedia. However, this may change in the future and the outcome will depend a lot on the quality of contributions. If you think that scholarpedia is a valuable resource, a good project and that you can contribute something, I'd say: Go ahead.
I also remember a quote by Gian-Carlo Rota: "You'll be better known for your expository work." I am not sure if this applies to everybody equally but it is a point.
What I find most interesting about wikis is that they are collaborative platforms with a public version history. This allows updates in addition to the "version of record" functionality of traditional publishing.
Scholarpedia has both, though if you are after Open Access in the sense of the Budapest definition (which allows reuse by anyone for any purpose), it is not there yet.
I am involved with a scheme in which the version of record (of review articles) is published classically in the journal, but in a way that allows the article to lead a second life as an updatable article on the English Wikipedia. Further details can be found here and here.
Both answers are excellent, I would like to add that today is too soon to answers because we don't know how the publication system will evolve.
Right now, we are following a traditional, centuries old system in with scientists gain reputation from their publications, which in very recent years were (and in some countries and some disciplines still are) just in paper.
Open access is "disruptive technology" for this system, but it may regard not only the licenses of research publications, but the very shape they can assume. There are experiments with peer review too. We can definitely imagine a future when sites like academia.se (or math.se, or others) will be taken into account for evaluation a scholar profile. For coders, is somehow customary to look at their GitHub or StackOverflow account...
And I remember at least one case (I don't have a reference, sorry) in which, among other things, a professor gained his tenure also for his concrete and excellent contributions to Wikipedia.
It is a matter of customs, habits, technology and culture of academia and his communities.
I want to focus on one point touched on in a couple of the other answers: wiki is a class of software that tends to have a certain set of features (though the features vary from one wiki to another). The technical features might impact the value to the audience, but I don't think they have inherent advantages or disadvantages like those described, from the perspective of the author.
A wiki-based publication, a traditional journal, or other formats may have any number of approaches to charges for publication, open access to readers, character limits, and may have varying reputation.
I'd urge PhD candidates considering questions like these to focus more on the specific publication, as measured against criteria like this, rather than worrying about the technical underpinnings of the journal. A publication's policies, processes, and record will have more of an impact on its value to you, than will the technology it uses.