Wiki

The three types of wiki only refer to the way in which you want to write it up. How you write it up is really determined by the way in which you want to use it. How do you want things like links and images to be structured.

The HTML way is to just use the TinyMCE editor which gives you the full formatting tools available on the Toolbar. You can, via the TinyMCE code, add or subtract toolbars and buttons as suits your individual requirements. For example, one of my clients wanted greater functionality for tables, to be able to add or subtract rows or columns. Going to the TinyMCE web site, the information I needed to add that fuctionality is readily available, so I found the relevant code in the /lib/editor/tinymce/lib.php file and added the "tablecontrols" button. (About line 139 if you are interested.) Works well, btw.

If you want your wiki to be more "wiki-like" then use either "wiki" or "creole" As far as I can tell, there is not much between  them. They appear, to me, to essentially be camel-case tools, but "creole" adds some formatting functionality not available in "wiki".  

There is no "Argument" for any particular type. For ease of use and familiarity, the HTML option is probably best. The learning curve is low, users are already familiar with the structure and use of toolbars and buttons. Not so for the other types. Basically, what it boils down to is personal preference. 

Personally, I rarely use a course based wiki. They are ugly and the collaborative approach to learning it encourages might be great for advanced learners, but I mostly deal with adolescents who think their lives are based on an appallingly bad American sit-com. That is how they talk to each other, that is how they percieve each other and if their day is not broken down into 30 minute blocks, including adds, chock full of abuse and pathos, they think they are boring failures. This promotes verbal bullying and it shows in their comments towards their peers - they think it is witty, or even funny, a sick-sad world. My preference is a site wide wiki, that is either fully integrated into Moodle, or can be accessible from Moodle without having to login or out and keeps logged in to both at the same time, but this does not appear to be a popular choice for some reason.

As I want my students to predominantly be responsible for a 'page' each; then I've decided to leave it open & let the page owner decide what he/she prefers. 

We've not really started that part of the assignment yet; so can't yet tell how it will work; but I'll point out that if they're used to (or want to get used to!) editing Wikipedia, then Creole/nWiki is a good idea; if they're not so bothered, then HTML is more like the message box in Moodle they're getting used to, so that's got its advantages.