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Googleguy posted to the effect that this was under-utilised screen real estate. Not everyone agrees. Oh, and welcome to WebmasterWorld!
There is none whatsoever. They are completely different implementations of search, running on different data.
The ODP search has been down before; when there are major system changes at the ODP (such as the recent charset conversion), search is usually one of the last things to be tested and debugged.
And ODP editors have always had a longer list of wishes than AOL had programmers--that's not "defunct", it's a sign of vitality. When nobody CARES whether a system works or whether it should do more, then it's time for its wake.
1. Use the Google directory search. Not as up-to-date as the current OPD, but may be usable for what you want. If it isn't usable for what you want, send Google an email to their "how can we improve search?" feedback address.
2. use any other clone of the ODP that is more recent and has a search facility:
3. Download a copy of the DMOZ RDF and search on that: