Napoleon's two paintings depict two different faces of his personality. The painting by David shows Napoleon imposing, victorious on his horse, exuding confidence and prosperity. This painting shows Napoleon's face that was unbeatable in his victories and had the strength and elegance of a great leader.
On the other hand, Delaroche's painting shows a downcast and poor-looking Napoleon, because Delaroche wanted to show that even with so many victories, Napoleon was a human being like anyone else, with pain, tiredness and sadness.