To start with the question: would it be more challenging to work as a project manager in either Matrix or Project-based organization? I think it will be so, based on more documents needed to practice the project management. For example, aside from Project Management Plan; Risk Management Plan, there are also Preliminary Gantt Chart, WBS, Network Diagram are required, instead of DID.
The second question: What complications can arise from one more than the other in the point of view of a project manager? I think this question always bothers the matrix organization since actually there may be too many people are in charge for the purpose of covering multi-aspects of the projects. As a result, no one has a general control power over the project. This problem will cause more disagreements that could postpone the milestones greatly.