Is IE the only web browser that requires <script></script> and hates <script/>?
No, all current browsers behave the same when being served XHTML as text/html. There is only a difference between browsers unless you are sniffing for IE and sending it a different Content-Type to other browsers. (Top tip: don't do that. There is nothing to gain and plenty of weirdness to get bitten by.)
The empty element syntax is not understood as anything special by HTML browsers, it is only there to paper the cracks between HTML's unclosed elements and XHTML's empty elements. So you can't ever use one as a ‘shortcut’; empty elements can-only-and-must be used for empty elements, as specified in the XHTML Appendix C guidelines.
You can verify this as simply as:
<p style="color: red" />html
All browsers I have tested colour ‘html’ in red.