You want your closing statement to be the Mariano Rivera of letters of intent: a clean win, effective, and unambiguous. Don't overthink it! Basic, professional closings are the way to go.
In the bad example, Jean is too vague, and has a few red flags, like suggesting that her last job didn't end well, and making an inappropriate joke about Scorpios to gloss it over. You can tell people you're great, but it's better to prove it by offering specifics, like she does in the better example. In the second example, Jean's letter body is more clearly organized, and makes sure to give the most relevant details about her career so far.