The 404 page that JIRA serves is a well composed, branded error page that is pleasant for customers to look at. The 500 page is not, and contains a dump of sensitive information. I've had to substitute in a custom 500 page to prevent our system information showing up to external customers, but it lacks the verve of the 404 page.
If you're using jira 6.1.x there is error500.soy file located in WEB-INF/classes/templates/jira/errors folder that you can customize
If you're on JIRA 6.0.x there is a 500page.jsp which you should customize to meet your needs - just search where exaclty it is located on the file system.
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