Assuming you want to click a Button to update:
private void RemoveCBDuplicates_Click(object sender, EventArgs e)
{
var itms1 = TheFirstComboBox.Items;
var itms2 = TheSecondComboBox.Items;
foreach (var itm in itms2)
{
if(itms1.Contains(itm)) itms1.Items.Remove(itm);
}
}