Differences in responsibilities of project manager between agile and traditional project management

There are no differences at all. And that is because agile project management or traditional project management do not exists. What exists is project management following some of the guides of principles you want (PMI, IPMA, GPM, PRINCE2, etc) inside an environement where an specific approach is taking (agile, waterfall, V, etc) and an specific project life cycle is taking. If you understand that, you will not fail.

Yes, same responsibilities, but can be much higher workload- for instance waterfall usually involves organising resources for just one round of user testing, but for agile it can be 6-8-10 or more rounds... Also the flexibility of agile means more effort managing that flexibility with senior stakeholders.

Responsibilities are more likely to vary from company to company than across PM methodology styles. In some companies, the PMO assumes responsibility for some aspects of projects. In other companies, with no PMO, the PM will have much greater responsibility. Another influencing factor is the degree to which the organization is matrix-based or traditional hierarchical.