Hi Cyril,
basically, both systems try to achieve the same goal, XML and zip instead of proprietary formats for storing documents. I believe the main difference is that OpenDoc is an open source initiative, and OpenXml is owned by Microsoft (you don't need a license though, it is fully 'open').
The reason OpenXml exists is the demand of us, the users, to drop the closed source 'doc' formats and Microsofts need to provide 'full fidelity', e.g. support for all the different things you can do with MS Office. It is highly unlikely that OpenDoc will provide that full fidelity support, as it is being developed by a large number of companies. OpenDoc has fewer schemas to work with, e.g. it is less-defined than OpenXML. Various OpenDoc supporting products do things differently with regards to undefined features that the product supports, but the OpenDoc standard doesn't.
Read up on this on Brian Jones' blog, he points out a number of features which are possible in Word / Excel / Powerpoint, but are unsupported by OpenDoc.
There will be support for OpenDoc in MS Office though, mainly because the demand exists inside governements and such.
Any Microsofteer who want's to acknowledge / refute these claims? As I haven't built either standard :)
The plain-text "Open XML" format aims to solve those problems and ... instead of using the OpenDocument format that many other software vendors support. ... older version of Word (or a different word processor) you have two choices