The most straight-forward approach is to do a second if-test but with the condition inverted. This technique is shorter, easier on the eyes, and easier to get right than a choose-when-otherwise nested block:
<xsl:variable name="CreatedDate" select="@createDate"/>
<xsl:variable name="IDAppendedDate" select="2012-01-01" />
<b>date: <xsl:value-of select="$CreatedDate"/></b>
<xsl:if test="$CreatedDate > $IDAppendedDate">
<h2> mooooooooooooo </h2>
</xsl:if>
<xsl:if test="$CreatedDate <= $IDAppendedDate">
<h2> dooooooooooooo </h2>
</xsl:if>
Here's a real-world example of the technique being used in the style-sheet for a government website: http://w1.weather.gov/xml/current_obs/latest_ob.xsl