Please use cdate(ddldate.selecteditem) for comparing dates.
Private Sub ddlDate_SelectedIndexChanged(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles ddlDate.SelectedIndexChanged
Dim expenddt As Date = Date.ParseExact(ddlDate.SelectedItem, "dd-MM-yyyy", System.Globalization.DateTimeFormatInfo.InvariantInfo)
txtValue.Text = expenddt
If Date.Today > CDate(ddlDate.SelectedItem) Then
MsgBox("The current date is greater than of selected date")
End If
End Sub