Compare Two Select Lists, and Require User to Select Different Values Use case:  I'm presenting the User with two Select Lists populated with the same People names.

The first select list is Primary Person, the second select list is Backup Person.

The User must select a different value from each list. The same Person can't be a primary and backup. If the User attempts to save the page using the same value, Drupal will throw an error.

What's the best approach?
For the Drupal form API, this would be handled with your validation handler. Have it check your 2 form values for equality, and throw an error if so.

function MYFORMBUILDER_validate($form, $form_state) {
  if($form_state['values']['person_primary'] == $form_state['values']['person_backup']) {
    form_set_error('person_primary', t('The primary and backup person must be different'));
    form_set_error('person_backup', t('The primary and backup person must be different'));
    array_pop($_SESSION['messages']['error']); //Remove duplicate message
  }
}