If I'm setting up a content-based site that I want to advertise on, is it typically better to use AdSense or should I look for an ad network that focuses on my particular vertical? Which one typically pays more?
I suggest you consider a third option. Think about the type of businesses that would benefit from advertising on your website, then contact those companies directly. The medium sized businesses will probably be the most responsive to this. Ask to speak to the person who handles their marketing. Tell them about your site and let them know that you are looking for advertisers, but you are not sure what the going rates are, then ask them if they'd be willing to make you an offer for sponsorship advertising on your site.
In my opinion this method will almost always bring in more money than going through AdSense or niche networks.