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.
Without job-level specifics, it can be tempting to get stuck in an "I'm awesome" loop without giving enough specifics. If you have a general idea of what job groove you'd be seeking at this particular company, build your letter body around that. If you're truly just trying to get a foot in the door at a company, you can use clues from your research about the company. What does their website say about their mission and priorities? What do current and past employees say about the company in online chatter? Even without specifics, you can cobble together a pretty good idea of what the company is seeking in potential employees. Sell your skills and experience points that are special to you, and especially relevant to your industry.