If your environment supports EL 2.2, just call its toString() method directly.
<c:if test="#{bean.myDate.toString() eq 'Wed Jan 01 00:00:00 CET 1001'}">
If yours doesn't, convert it to String first by inlining it as body of <c:set>.
<c:set var="myDate">#{bean.myDate}</c:set>
<c:if test="#{myDate eq 'Wed Jan 01 00:00:00 CET 1001'}">
Unrelated to the concrete problem, this is a rather strange way of comparing dates. It's very sensitive to changes in locale and timezone (if the webpage visitor uses a non-English locale and your webapp supports non-English locales, then the test on Wed Jan would fail and if the webserver is moved to non-CET timezone, then the test on CET would fail). Don't you rather want to compare it on year 1001 directly or a fixed pattern such as 1001-01-01 or so? Further I also wonder why you don't do the test in the rendered attribute of the JSF <h:outputText> component.