I work in a matrix organization, where employees may report to many managers, for example in my case I work as design engineer in a functional department sometimes the company gets a project that needs a design engineer to assist the “project manager” (senior process Engineer because we do not have PMs) on certain tasks. I may be assigned to the project for a short time, or they may transfer me there while my services are required. If I am assigned there for a short time, I have to report to two bosses. Some of the advantages are that information flows through the organization, employees are in contact with many people and resources can be used efficiently, since experts and equipment can be shared across projects.
I do not have experience with the other types of organizations but I am not totally comfortable with the matrix since employees may have to report to two managers, which adds confusion and may cause conflict. If priorities are not defined clearly, people may be confused about their role and responsibility. If any resource is scarce there may be competition to use it, which may cause hostility. Finally but not less important in a matrix organization, workloads tends to be high. Employees have to do their regular work along with the additional project which can exhaust people affecting productivity.