The same XWiki installation I use with different DB prefixes for some tests. By accident I discovered, that if DB name has no prefix, captcha works fine.
If I turn on db prefix in config files and reload xwiki, xwiki works fine, but captcha doesn't show any presence in registration form.
"Require captcha to register (Default: No)
Set this true to require the user to solve a captcha in order to register. NOTE: captcha.enable must be set true in the xwiki.properties configuration file in xwiki/WEB-INF/"
captcha.enable=true is added to xwiki.properties also as required in help file.
Tests were done with default DB names xwiki and prefixname_xwiki