A nomination post is basically a sales pitch, packed into 1200 characters. You need to persuade readers that you are or might be a good choice in a few hundred words (give or take). So a nomination is longer than an "elevator pitch" but shorter than a full bid.
Therefore, don't think of your nomination post as a complete nomination by itself. Instead, think about how to draw people in and steer them to more information. Some of those 1200 characters can be links, for example.
I've stood in three SE moderator elections and won all of them. Those three nomination posts were of different styles. As with any other type of writing (and, perhaps, especially important in an election), know your audience and context. What does your community value? What are people looking for in a moderator in this election? What is the community currently struggling with that you can help with? Answering those questions will help you frame your nomination post.
In a site's first election, consider focusing on your track record of moderation activities, by which I mean the things community members can do to curate the site, and broader experience (like on other SE sites) if you have it. Voters are electing the complete slate of moderators.
On a site with an established moderation team and policies, focus on how you fit into that -- how does adding you to the team make the team better?
On a site where the content is more analytical, objective, and evidence-based, use facts more and feelings-based appeals less. (Less, not none. For example, in this nomination I talked about personal background and attitude toward moderation style, even though I'd led with a facts-based case.) On a site that functions as a community of friends, consider reversing that -- but always keep in mind that the election is about the community, not you in particular.
On a site where you're well-known, you can probably spend less space on the "resume" part and more on how being a moderator and not just a high-rep user would benefit the community. If you're a relative newcomer or low-rep, on the other hand, put more work into establishing your credentials, so to speak.
Use humor sparingly unless you're sure you can get away with more. On Worldbuilding, one of the more whimsical sites, I ended an otherwise-straight nomination with "I like binary stars, sociology, and consistent magic."
Some nominations use the "pros and cons" format. I did that in my nomination on The Workplace, where I would have been comfortable with either outcome (winning or losing), but I don't think I would emphasize cons in a nomination where I really wanted to win. The community can already ask questions of candidates, so there are ways for drawbacks to come out. Don't hide stuff, but ask yourself if you want to spend your limited space in the nomination on negatives.