how to compare update_option() after it saves to database?

Looking at the full code in the updated question, it seems that you’re just checking if the option has been changed; so for that purpose, you could simply do so, where <option name> is the option name like my_option:

add_action( 'update_option_<option name>', function(){
    // you shouldn't echo, but this is just for testing
    echo 'option changed';
} );

And if the option’s value is actually the same as the old one, the above function won’t be called. Because that’s how update_option() works — if it’s called but no changes in the option’s value, then the hook update_option_<option name> won’t be called. And neither does the updated_option or update_option hook.

Now you said, “my option name contains user ID” and mentioned that the option name is <user ID>_interview_date. And in that case, you can do something like this:

• Option 1: Validates the user ID/data:

  add_action( 'updated_option', function( $option_name ){
      if ( preg_match( '/^(\d+)_interview_date$/', $option_name, $matches ) ) {
          $user_id = absint( $matches[1] );
          // Check if the user exists.
          if ( $user_id && ( $user = get_userdata( $user_id ) ) ) {
              // you shouldn't echo, but this is just for testing
              echo $option_name . ' option changed';
          }
      }
  } );
  

• Option 2: No validations..

  add_action( 'updated_option', function( $option_name ){
      if ( preg_match( '/^(\d+)_interview_date$/', $option_name, $matches ) ) {
          // you shouldn't echo, but this is just for testing
          echo $option_name . ' option changed; no validations performed..';
      }
  } );