I'm working on my own social media site, and when it comes to moderation - is a hierarchy of Administrators and Moderators better or worse than a democratic voting system similar to Stack Exchange's system?
In other words, when is it better to let the staff moderate, and when the community?
Your social media site is new/in development. Without a population of users to start out with, it's going to be a bit difficult to feature a democratic voting system purely because there aren't enough people to vote just yet.
I'm unsure if you've noticed, but CommunityBuilding.SE has had little traffic lately. Some actions, such as suggested edits, are sitting idle because few users with high enough reputation are reviewing these edits.
In the comments, you ask:
I'd like to know on this stage which community structure will succeed: So, a staff team, or the community, for the rulers?
The reason the simple "Administrator, Moderator, User" hierarchy is still around is because it works. If your website needs moderation, the easiest solution would be to start out with a simple hierarchy of Administrators and Moderators. These staff members would handle cleanup/maintenance of the site. The benefit of this process is that, provided your staff is active, problems are handled rather effectively.
The benefit of community-based moderation is that simple cleanup can take place without a moderator being present. Through this, a site that employs community-based moderation can become somewhat self-regulating. Additionally, your users will feel a sense of inclusion in the site's day-to-day operation. Not only are they contributing content, but they're contributing to its moderation as well.
The true answer to your question is that you should employ both of these structures. There are assuredly some moderation actions you don't want regular users to have access to (such as user suspensions, single-handed post deletion, etc.), but there's plenty that you can give them access to that would take the load off of your moderators. By benefiting from both moderation philosophies, you can ensure your site is well-maintained.
You also ask:
When is it better to let the staff moderate, and when the community?
Well... It depends, and as the developer/founder, it's up to you.
There's no easy answer here. My recommendation would be to start separating actions that moderators have access to and frequently use that are safe for community members to participate in.
For example, are moderators frequently deleting spam? Perhaps, once a post reaches a certain amount of spam-votes/spam-reports, it should be automatically locked/hidden/deleted.
Are moderators frequently moving posts to a different topic/category because it was posted in the wrong area? Perhaps users can have access to a voting process to move it to another category. If the yes votes outweigh the no votes, the post is moved.
There's no simple "This is better" answer. Dig into and get a feel for how your site operates. Determine where there's pressure, and see if the community can safely help out.
