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Lucene is much older than Xapian. It has been extensively deployed and has a lot of community support. It is implemented in Java, though, which might be a turn-off if you're not interested in maintaining Tomcat or other such containers.
Xapian is written in C++, an has bindings for several popular web scripting languages, which makes it attractive from a deployment perspective. It is also more modern and incorporates many powerful features. Deploying an actual search engine requires more setup than Lucene, which largely runs out of the box.
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