Use time
Let's say you have the initial dates as strings like these:
date1 = "31/12/2015"
date2 = "01/01/2016"
You can do the following:
newdate1 = time.strptime(date1, "%d/%m/%Y")
and newdate2 = time.strptime(date2, "%d/%m/%Y")
to convert them to python's date format. Then, the comparison is obvious:
newdate1 > newdate2
will return False
newdate1 < newdate2
will return True