Overstating your positive qualities while not providing supporting details can be as bad as not giving any examples at all. While this candidate thinks she is demonstrating her leadership skills, she’s actually not providing the AdCom with enough evidence to show how effectively she leads a team.
This candidate demonstrates his leadership qualities first by naming specific actions, then by supporting them through a career story. His anecdote not only shows that he led a team to success, but that his managers trust him with large projects and that he is especially good at communication and delegation. The AdCom will clearly understand the practical impact of his strengths.