Use a Letter of Intent if: You want to take serious steps towards negotiating the purchase of all or part of a company. You want to secure your interest in a company and request that the sellers exclude negotiating with another buyer.
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.