A Google Webmaster Help thread has discussion around Japanese domains and how Google may treat them. Honestly, I know very little about this topic, so I hope I do justice to this thread.
Example of Punycode domains versus Unicode:
- Unicode - http://アアアアア.com
- Punycode - http://xn--cckg5dfdwc.com
Google said, for "domain names in Punycode are equivalent to their Unicode versions." There may be an issue with PageRank being displayed in the Punycode version in the Google Toolbar, but Google assures us that there is PageRank, the equivalent to the Unicode version. JohnMu said in the thread that he would "pass that on to check out" why it isn't working properly in the toolbar.
So which should you use? Google said, they generally use the "Punycode versions since this is more likely to work across all browsers."
Forum discussion at Google Webmaster Help.