mysql> select date_format('2013-11-19','Y-m-d') > timediff('2013-11-19', '2013-11-20');                                        

ERROR 1267 (HY000): Illegal mix of collations (utf8_general_ci,COERCIBLE) and (latin1_swedish_ci,NUMERIC) for operation '>'

The language used for day and month names and abbreviations is controlled by the value of the lc_time_names system variable (Section 9.7, “MySQL Server Locale Support”).

The DATE_FORMAT() returns a string with a character set and collation given by character_set_connection and collation_connection so that it can return month and weekday names containing non-ASCII characters.

mysql> set names utf8;
mysql> select charset(date_format('2013-11-19','Y-m-d')), charset(timediff('2013-11-19', '2013-11-20'));
+--------------------------------------------+-----------------------------------------------+
| charset(date_format('2013-11-19','Y-m-d')) | charset(timediff('2013-11-19', '2013-11-20')) |
+--------------------------------------------+-----------------------------------------------+
| utf8                                       | binary                                        |
+--------------------------------------------+-----------------------------------------------+

mysql> set names gb2312;
mysql> select charset(date_format('2013-11-19','Y-m-d')), charset(timediff('2013-11-19', '2013-11-20'));
+--------------------------------------------+-----------------------------------------------+
| charset(date_format('2013-11-19','Y-m-d')) | charset(timediff('2013-11-19', '2013-11-20')) |
+--------------------------------------------+-----------------------------------------------+
| gb2312                                     | binary                                        |
+--------------------------------------------+-----------------------------------------------+

mysql> select date_format('2013-11-19','Y-m-d') > convert(timediff('2013-11-19', '2013-11-20') using utf8);
+----------------------------------------------------------------------------------------------+
| date_format('2013-11-19','Y-m-d') > convert(timediff('2013-11-19', '2013-11-20') using utf8) |
+----------------------------------------------------------------------------------------------+
|                                                                                            1 |
+----------------------------------------------------------------------------------------------+