What is as responsibility for teams running private cloud servers that is less of a concern when running in the public cloud?

Cost is a significant concern in both private and public cloud environments, although the models and control over spending differ.

Metrics and monitoring are crucial responsibilities in both private and public cloud environments to ensure performance, health, and security, though the tools used may vary.

In a private cloud, the organization is entirely responsible for the physical hardware, its maintenance (including repairs, upgrades, and disposal), and underlying infrastructure like power and cooling; in a public cloud, the provider handles these physical aspects.

Credentials management remains a shared responsibility, with significant customer involvement in managing access to their resources, even in the public cloud.