Re: 中国 and 中國
Check the whois of any IDN.cn at CNNIC and you will see that both are granted with one registration.
For example, 虎.cn (tiger) shows that these three domains are granted with one registration.
So, answering your questions, both will be used, .中国 by those who use Simplified Chinese and .中國 by those who use Traditional Chinese. Which is better? Depends, but not an issue since both belong to the same person by default.
IDN? What's an IDN?