The advantages of a functional organizational structure include:
- Team members don't have the "more than one manager" problem: In a functional organization, team members know that their functional manager, and only their functional manager, has authority over them.
- Project managers cannot abuse their team members: Since the team members belong to the functional manager, it is impossible for the project manager to abuse them (forcing them to work overtime because of an unrealistic schedule) - they know that someone (the functional manager) will stand up to the team members.
- Centralized resource pool: When a project manager needs resources, he asks the functional manager who allocates resources to the project manager based on their availability. This is extremely critical in the absence of a PMO (who will take this role in projectized organizations) - this will avoid conflicts in resource allocation.
Disadvantages of a functional organizational structure include:
- Not getting the best resources for the project: Functional managers sometimes give their worst resources to the project managers, because either they want to get rid of them for some time or they want them to learn and get some experience while working on a project.
- No authority for the project manager whatsoever: The project manager, in a functional structure, doesn't have any authority over the resources (all the authority belongs to the functional manager). This often leads to insubordinate resources.
- Potential abuse by the functional manager: The functional manager can abuse his power by blocking access to some critical resources by the project manager, maybe claiming that the functional manager needs them to work on some "very important" tasks.
- Working in silos: In a functional organization, resources work in silos, they rarely, if ever, interact with resources falling under a different functional manager. This means that these "dispersed" resources don't pollinate each other with experience.
There are many other advantages and disadvantages of a functional organizational structure, but I've listed the ones that I know of (from a project manager's perspective, since I'm a project manager).
I personally don't think a functional organizational structure is ideal for project managers - better go with a matrix organization. The best organizational structure for project managers is the projectized one.