For the record, there is no difference between the two statements.

Code:
SQL> SELECT TO_CHAR(sysdate-1440/1440,'DD-MON-YY HH:MI:SS pm') FROM DUAL;

TO_CHAR(SYSDATE-1440/
---------------------
19-JUN-03 03:45:54 pm

SQL> SELECT TO_CHAR(sysdate-1,'DD-MON-YY HH:MI:SS pm') FROM DUAL;

TO_CHAR(SYSDATE-1,'DD
---------------------
19-JUN-03 03:45:54 pm

So where TO_char(date_field) > SYSDATE - 1; is the same as
   where TO_char(date_field) > SYSDATE - 1440/1440;