With the increasing adoption of private cloud infrastructures by providers and enterprises, the monitoring of these infrastructures is becoming crucial. The rationale behind monitoring is manifold: reasons include saving energy, lowering costs, and better maintenance. In the e-Science sector, moreover, the collection of infrastructure and application-specific data at high resolutions is immanent. In this paper, we present two monitoring approaches implemented throughout two European projects: ECO2Clouds and EXCESS. The ECO2Clouds project aims to minimize CO2 emissions caused by the execution of applications on the cloud infrastructure. In order to allow for eco-aware deployment and scheduling of applications, the ECO2Clouds monitoring framework provides the necessary set of metrics on different layers including physical, virtual and application layer. In turn, the EXCESS project introduces new energy-aware execution models that improve energy-efficiency on a software level. Having in-depth knowledge about the energy consumption and overall behavior of applications on a given infrastructure, subsequent executions can be optimized to save energy. To achieve this goal, the EXCESS monitoring framework provides APIs allowing developers to collect application-specific data in addition to infrastructure data at run-time. We perform a comparative analysis of both monitoring approaches, and highlighting use cases including a hybrid approach which benefits from both monitoring solutions.