Compare Two Select Lists, and Require User to Select Different Values
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
  }
}