I posted two maps in the Insight Maps section of the website (see also below). They are identical in content but the layout/presentation of the information is very different: one has a more traditional horizontal layout and one has a circular layout.
I don't have a strong preference and the layout I pick often depends on the content. Some content lands itself to a circular layout and others don't. The maps I posted depict what could be considered an iterative, circular process, and therefore the circular layout made sense. However, for the sake of presenting new information to people, I would opt for a more traditional layout unless the target audience is already very familiar with my mapping approach.
When facing such a map for the first time, people will often ask, "How do I read this?" or "Where do I start?" because they are so used to reading from top to bottom and left to right. A traditional horizontal layout allows them to do that to some extent even if the content doesn't look like a traditional piece of paper with lines of text. Therefore, the traditional layout is more approachable, I believe and quite useful for audiences not accustomed to these maps. People get most confused when I have what looks like a horizontal layout, yet one or more arrows point up instead of down. They immediately assume it's a mistake.
Click on the image to view the full map.