MoinMoin and Distributed Wiki appear to be very similar. Both are written in Python, provide a hierarchy of wiki pages, page versions, and are customizable. But they are conceptually very different and they target different markets.
They are also very different conceptually. At its core, MoinMoin is a list of wiki pages. Because page names can share substrings, it supports simple hierarchies. In contrast, the Distributed Wiki is a tree of content types, a first cousin to Plone. Not just a CMS, but a complete web development environment.
The difference is very clear when dealing with larger hierarchies. Here is a tree of over a 1000 items, built using the DIstributed Wiki. A basic principal in human factors is that no category should contain more than about 7 items. So the Distributed Wiki has very deep, but easy to understand hierarchies. In contrast MoinMoin handles this list of 486 items mostly as a list. There is a little bit of hierarchy in the list. I tried reading through it, but it really is way way too much for the human brain to make sense of. Rather than being sorted alphabetically it should be a deeper tree of categories.
MoinMoin has very few content types. Maybe a wiki page, and a file or image. Content types are very powerful. For example the Distributed Wiki has a Google Maps content type. Here is an example of hierarchical maps running on an older version of the software.
Being browser editable is very powerful. There was a recent MoinMoin discussion about being able to modify favicon.ico. They had to make some changes to make it possible for developers to git clone the repository, edit the Python, and change the favicon. In the Distributed Wiki, an end user just use the Web GUI to delete and upload a new favicon. Much easier. A lot more people can do that.
The two products are at different stages in the life cycles. MoinMoin is old mature software. The above list of feature requests shows how it may evolve in the future. The distributed wiki has just been released. It is not "just a wiki". It is a complete web development environment. We have no idea what new content types, and distributed content types will be released.