On desktop, the privacy shortcuts selection from the dropdown takes you to a privacy checkup, which acts more like a FAQ than an actual menu to change any settings. In the mobile app, though, you'll have quick access to making your account more secure (adding two-factor authentication and controlling who sees your posts, among other tools). The big addition to the privacy center though, is being able to delete anything you've shared or reacted to, and your search history.
Facebook also made it easier to inspect how you're advertised to. There are options for changing how you're tracked and advertised to on the greater web. You can also download a copy of your Facebook data (photos, contacts, timeline posts). If you don't think this goes far enough, or just don't trust Facebook at its word, there are browser extensions for blocking Facebook's data-sharing. Facebook said that previously, all these functions were spread across "nearly 20" different screens on mobile.
One thing that isn't any easier? Deleting your account. The only option offered via the general account settings page is deactivation, which simply hides your account rather than removing it wholesale. You still have to Google for the deletion page, then make a request manually and wait up to 90 days for the process to take place. This obfuscation has been around for a while now, and likely won't change anytime soon.