One big advantage of JavaDocs is that they just work. Everything needed to build and view them is included in the JDK that you already need to have installed for compiling your programs.
Doxygen, on the other hand can be a pain to set up and get working correctly. but if it is set up correctly it should be able to generate PDFs, RTFs, and DocBooks, as well as HTML. The HTML is not organized as well by default as JavaDocs since the index.html brings up a blank page by default. Also, inline classes and static members may need special flags to be included in documentation, and if you want to generate a PDF you may have to deal with hassles of your distribution of Linux not having the needed pdflatex command (e.g. Ubuntu/Mint have had problems recently) so if you just apt-get install it and run you may get a screen full of errors even with a simple program. Compared to the ease of getting javadoc automatically when you install the API, Doxygen setup can be a miserable experience. Once you overcome the hurdles, it should be more flexible in dealing with projects involving more than just java, though.
