Are companies more effective if they operate on a centralized or decentralized structure, and how do they determine which one works best?
This is an excellent question and part of your answer is embedded in your question. Sometimes a centralized structure is needed for a company to function properly. When things are in disarray and decisions need to be made, a centralized structure might be the better approach. For smaller companies, this might be a good approach, especially if you have a great head. However, at times, a decentralized structure is more necessary. As you can imagine, a lot of red-tape and bureaucracy can be circumvented and this can make things more expedient and creative.
In terms of what is best for a given company, this is a complex issue. There are several factors to consider. First, size is important. The larger a company, the less centralized it should be, even for practical reasons. Second, talent is important. The more talented people you have, the more autonomy you might want to give.