Inception and general approach:
You can broadly say that Facebook first copied Friendster (the CEO openly admits this) before going over to Facebook on a regular basis (apps, share function, like function, LBS, real-time elements, feed system, Mixi Connect etc.).
Mixi today is Japan’s only social network providing a true social graph, meaning the people you befriend are usually your real friends – like on Facebook. GREE and Mobage-town are called social networks by some and mobile gaming communities by others. I prefer the second description, as the focus here is on gaming. Both platforms offer a mix of social and virtual graph, meaning you befriend avatars (strangers), not only your friends in real life.
Registration and privacy:
Due to strict local youth protection laws (that don’t affect Facebook Japan by the way) and online privacy concerns Japanese web users have in general, registration isn’t simple.
Until 2008, you couldn’t become a member unless an existing one invited you. Today, self-registered members must acquire another member for Mixi quickly or they will get banned, for example.
Still, Mixi requires new users to provide a Japanese cell phone number and mobile email address – otherwise, it’s impossible to register.
In other words, having multiple or ghost accounts (and causing trouble or messing up user stats) is far easier on Facebook than on Mixi.
It’s also worth noting that apart from the Japanese original, there is only a Chinese version of Mixi available (Mixiu) – quite a contrast to Facebooks hyper-internationalization in recent years. As a consequence, Mixi can only count 21 million members (99% of whom are Japanese), as opposed to the 500 million+ users Facebook currently boasts worldwide. Needless to say, this heavily affects user behavior.
Mixi announced internationalization plans recently (see my answer to).
As Yuriko hinted at, Mixi is largely mobile now (GREE and Mobagetown’s PVs are around 99% mobile-based).
To be more specific: In July 2010 (latest data available), Mixi had 30 billion page views, and just 5.23 billion of these came from PCs.
What’s interesting is that Mixi in September 2007 had 12.3 billion page views, 5.9 billion of which came from PCs. This obviously indicates that a large number of Mixi users migrated to cell phones in recent years.
And there are many more differences. I hope it’s OK to offer a link to my primer on Mixi on TechCrunch:
Asiajin, a blog focused on Japan’s web industry (and which I also write for) provides a large number of articles about Mixi as well (in English): http://asiajin.com/blog/tag/mixi/