From their website:
Although battle plans specify which commanders to use, advanced players will soon be paying attention to what specific commanders bring to the table when playing skirmishes, player-created scenarios, or other battles where players can choose which commanders to employ.
The biggest difference are the cards that a commander will “donate” to the Leadership deck. This deck is comprised of ten basic cards that each House has in common. However, each commander also has 5 cards which are included when he is present in the battle. By learning which commanders’ cards work well together with your particular play style, you’ll gain an advantage when you have an option to recruit your choice of commanders.