Solution 1:

auto_now takes precedence (obviously, because it updates field each time, while auto_now_add updates on creation only). Here is the code for DateField.pre_save method:

def pre_save(self, model_instance, add):
    if self.auto_now or (self.auto_now_add and add):
        value = datetime.date.today()
        setattr(model_instance, self.attname, value)
        return value
    else:
        return super().pre_save(model_instance, add)

As you can see, if auto_now is set or both auto_now_add is set and the object is new, the field will receive current day.

The same for DateTimeField.pre_save:

def pre_save(self, model_instance, add):
    if self.auto_now or (self.auto_now_add and add):
        value = timezone.now()
        setattr(model_instance, self.attname, value)
        return value
    else:
        return super().pre_save(model_instance, add)

Solution 2:

These fields are built into Django for expressly this purpose — auto_now fields are updated to the current timestamp every time an object is saved and are therefore perfect for tracking when an object was last modified, while an auto_now_add field is saved as the current timestamp when a row is first added to the database and is therefore perfect for tracking when it was created.

Solution 3:

According to the django documentation using both auto_now and auto_now_add in your model fields as True will result in an error because they are both mutually exclusive.

Solution 4:

As Official Django documentation says -

auto_now, auto_now_add and default are mutually exclusive and will result in an error if used together