This transformation doesn’t need any conditional XSLT instructions at all and uses no explicit priorities:
<xsl:stylesheet version="1.0"
xmlns:xsl="http://www.w3.org/1999/XSL/Transform">
<xsl:output omit-xml-declaration="yes" indent="yes"/>
<xsl:strip-space elements="*"/>
<xsl:template match="node()|@*">
<xsl:copy>
<xsl:apply-templates select="node()|@*"/>
</xsl:copy>
</xsl:template>
<xsl:template match=
"*[not(@*|*|comment()|processing-instruction())
and normalize-space()=''
]"/>
</xsl:stylesheet>
When applied on the provided XML document:
<Person>
<FirstName>Ahmed</FirstName>
<MiddleName/>
<LastName>Aboulnaga</LastName>
<CompanyInfo>
<CompanyName>IPN Web</CompanyName>
<Title/>
<Role></Role>
<Department>
</Department>
</CompanyInfo>
</Person>
it produces the wanted, correct result:
<Person>
<FirstName>Ahmed</FirstName>
<LastName>Aboulnaga</LastName>
<CompanyInfo>
<CompanyName>IPN Web</CompanyName>
</CompanyInfo>
</Person>