I think Project-based Organization manager is better than being a manager in a matrix-organization.
A project-based organization manager have a lot of power and easier to run projects because the entire structure is set up for that purpose. Also, in project-based organization, managers have a high level of
authority to manage and control the project resources. The project manager in this structure has total authority over the project and can acquire resources needed to accomplish project objectives from within
or outside the parent organization, subject only to the scope, quality, and budget constraints identified in the project.
But as a matrix-organization manager, project managers may or may not have a lot of power, and because of its complex structure, both the project and functional managers must be certain that they have touched bases with each other for any major decisions in their areas of responsibility. Even if there is a balance of power for each manager in the matrix organization, the people still asking who is the real boss?!
So, it is clear that to be a project-based organization manager is better.