Advantages: The primary advantage of this style of campaign design is that the DM can immediately focus on campaign elements that the players will interact with directly. By starting small and focusing on material that is going to be directly useful to the players the DM can avoid potentially wasted effort and concentrate on writing down stuff that is directly relevant to the adventures that take place during the game sessions. This form of design style usually works well for campaign settings that are developed "on the fly" while the actual campaign is being played, which points to another advantage of this type of design method: you can jump in right away and begin putting people around the table to roll dice and slay villains without needing too much lead time.
Disadvantages: The obvious disadvantage to this sort of campaign design method is that because you are developing your campaign as you go, it is easy for continuity errors to crop up as later designed material contradicts earlier designed material. In that case, you would need to either discard your cool new idea because it contradicts material you already wrote or go back and fix the earlier details that are now contradicted. This can be an especially thorny issue if you are designing the campaign setting while also running actual game sessions in the setting, in which case the players have probably already seen the now potentially invalid material. In some cases this accidental contradiction could provide a potential adventure hooks as the mystery of why (for example) halflings now all have lavender hair could be a topic that fuels investigation by the players. Another disadvantage of this style of campaign design is that long term planning is difficult. Trying to plan a long term campaign plot for the players to follow, or including an archenemy is difficult when you don't have the campaign parameters worked out in advance. This dovetails with yet another disadvantage of this type of campaign design - new elements can seem forced and artificial when they are introduced to the setting. If the first time the characters hear of the nation of Goblivania is when it is revealed that the Duke's trusted adviser is a spy for that nation, then the revelation will probably have little impact on the players. It takes time to build up some ire, and when a DM starts introducing elements on an ad hoc basis they run the risk of having the players react with indifference.
Advantages: The central advantage of this style of setting design is that it provides a comprehensive framework for the game world. A world designed from a "Top-Down" perspective will likely have better cohesion with specific elements "fitting" better into the whole. Because the campaign world has a ore or less fleshed out framework, the DM is better able to create large scale plots and find lots of potential adventure hooks. Because much of the groundwork has been laid down in the setting development process, if the players decide to go off on a tangent, the DM won't be caught flat-footed and stuck trying to fill in the gaps in a hurry. Yet another advantage is that creating campaign setting material is fun. At least I find it fun. And building an entire game world in toto gives lots of opportunities to do just that.
Disadvantages: Even though creating an architectural framework to hang your campaign sessions on is quite useful, there are a number of disadvantages. The first is that when confronted with a blank page and the need to build an entire world, a DM can feel overwhelmed by the volume of work needed to prepare the setting. Knowing when to leave things vague at the edges and avoid getting bogged down in unnecessary detail is an acquired skill. Once a DM starts building an entire world, it is easy to get into the weeds developing material that the players will never see, will never affect them, and which if they did, they probably would not care about. The players probably don't need to know about the price of broccoli in a country a hundred miles away from them, and probably would find it to be tediously boring if you told them. The real danger of this sort of far ranging design is that after a DM has put a lot of effort into defining the number of dresses owned by every one of the Queen's ladies in waiting there is a great temptation to try to wedge this information into the game session in order to show all the work off to the players. A second problem is that this style of campaign design may curtail spontaneity and provide a setting that isn't as able to bend to accommodate the flow of the actual campaign. Because so much is predefined, if the DM has an interesting idea after the setting has been developed and details relayed to the players, there may be no good way to incorporate the idea into this particular setting. Another disadvantage is that this style of setting design requires a fair amount of preparation. Because you are starting the design process at such a large scale, it takes some time to work down to the level where you are actually ready to sit down with a group of players and engage in gaming sessions.
As I said before, there is no right way or wrong way to design a campaign setting, it all comes down to personal preference. I like designing top-down, but I often mix and match, jumping back and forth between large scale elements and tiny details on a regular basis. As I go through the process of designing my new fantasy campaign setting, I'm sure I will do this several times.
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