OpenXML is the file format Microsoft has proposed as a standard for document formats. Although offered by Microsoft as a standard, it has a strong Microsoft product bias. OpenDocument is a competing standard, sponsored by companies like IBM and Sun, without a bias toward any particular office product suite.
There are converters for both Microsoft Office and OpenOffice that will read/write both formats, so it's probably not critical about which you choose. Most open source-oriented people favor OpenDocument, as single vendor-sponsored standards typically end up favoring their products.
The challenge with converters tends to be how accurately they reproduce document formatting, so it's important to evaluate how well these converters might work for you, given your use cases. It's early days for these particular converters, and they'll undoubtedly improve over time.
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