with doxygen it is easier to maintain documentation and to support contrib modules
reference is always consistent with the code (for example, it can not contain function which have been deleted)
generator has some built-in correctness checks (for example, if some function have several documented parameters and several undocumented, then generator will produce a warning)
Main disadvantages:
no pdf documentation yet (doxygen supports this output, but it needs some tuning)
no java/python documentation yet (doxygen can produce xml, but some cooperation with javadoc/pydoc/epydoc is needed)
basic search is limited to entity identifiers only, i.e class/method/namespace/tutorial names (Google custom search can be used for full-text search)
Additional advantages:
doxygen can produce help in some additional formats: rtf, chm (Compiled HTML), qch (Qt help), Eclipse help, XCode DocSets. However, all these methods should be additionally configured and tuned
basic search works without web server (one can build and use html reference on local machine)
formula rendering uses MathJax client-side technology
html documentation can be built really fast comparing to sphinx (1 min vs. 31 min)
