In the game, you use critical stars for extra damage. Jeanne Alter has a skill that further increases her critical damage, making her one of the most prolific user of the crit stars. Normal Jeanne can automatically produce stars with one of her skill, hence the first dialogue.
Also, Jeanne Alter has a skill that increases attack for the whole party with additional boost to characters with dragon attribute. Normal Jeanne doesn't have that attribute, hence the costume.