A specific difference is that the XnViewMP supports more file formats than the free version (XnView). According to the developer's information, XnViewMP supports 500 file formats. For a few of them, you can also perform editing. There is also a table with all this information on the official website.
Supported formats page: http://www.xnview.com/en/xnviewmp/#formats
Additionally, the XnViewMP is not free. All the features in XnView are present in the MP version, only that they're tweaked and enhanced a little.