They are the same. This can be seen by running the EXPLAIN command:
mysql> explain Select * from Table1 T1
-> Inner Join Table2 T2 On T1.ID = T2.ID;
+----+-------------+-------+-------+---------------+---------+---------+------+------+---------------------------------------------+
| id | select_type | table | type | possible_keys | key | key_len | ref | rows | Extra |
+----+-------------+-------+-------+---------------+---------+---------+------+------+---------------------------------------------+
| 1 | SIMPLE | T1 | index | PRIMARY | PRIMARY | 4 | NULL | 4 | Using index |
| 1 | SIMPLE | T2 | index | PRIMARY | PRIMARY | 4 | NULL | 4 | Using where; Using index; Using join buffer |
+----+-------------+-------+-------+---------------+---------+---------+------+------+---------------------------------------------+
2 rows in set (0.00 sec)
mysql> explain Select * from Table1 T1, Table2 T2
-> Where T1.ID = T2.ID;
+----+-------------+-------+-------+---------------+---------+---------+------+------+---------------------------------------------+
| id | select_type | table | type | possible_keys | key | key_len | ref | rows | Extra |
+----+-------------+-------+-------+---------------+---------+---------+------+------+---------------------------------------------+
| 1 | SIMPLE | T1 | index | PRIMARY | PRIMARY | 4 | NULL | 4 | Using index |
| 1 | SIMPLE | T2 | index | PRIMARY | PRIMARY | 4 | NULL | 4 | Using where; Using index; Using join buffer |
+----+-------------+-------+-------+---------------+---------+---------+------+------+---------------------------------------------+
2 rows in set (0.00 sec)