There is no difference in add due to auto boxing/unboxing. Actually don't do new Integer(12) but Integer.valueOf(12) since it uses the flighweight pattern and reuses known objects (in the range -128, 127). So no new object would be created.
There is a difference in remove for example.
Since if you intent to call remove(Object) calling remove(5) will call remove(int index) and this perhaps is not what you want.
You should do remove((Integer)5) if you want to remove the number 5 or remove(5) if you want to remove the fifth element.