Mutli-domain monitoring aims at guaranteeing QoS for services crossing several domains. It is often desirable to perform global monitoring to guarantee end-to-end QoS for services across domains and to reduce the monitoring cost. However, global monitoring might be infeasible due to confidentiality constraints. The alternative solution is to perform per-domain monitoring. In this work, we propose to evaluate global and per-domain monitoring techniques. For this end, we study the properties of multi-domain networks and the requirements of multi-domain monitoring. We formulate the problem as an Integer Linear Program (ILP). We show that it is a Nondeterministic Polynomial Time Hard (NP-Hard) problem, and therefore, we devise a heuristic that meets multi-domain properties. We show that confidentiality is far from being the only constraint to global multi-domain monitoring. In our evaluation, the confidentiality constraint has been relaxed, in order to investigate other performance metrics; namely, the monitoring cost, the quality of monitored paths, the anomaly detection delays, and the fairness of monitoring load distribution among domains. Simulation results on random topologies show that per-domain monitoring outperforms global monitoring for all these metrics, except the monitoring cost that is slightly lower for global monitoring.