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)