In case of Reading the Excel file,
The most important difference is that JXL does not support xlsx file format. Wheres POI supports old xls and the xlsx format as well.
In case of creating the Excel file,
POI has rich API that supports conditional formatting, rich text formatting, Chart creation and many more other features.
POI has the more extensive set of documentation and JXL is not very much maintained and updated, where POI is maintained very well.
So, my vote goes to Apache POI library.