The digital transformation of education demands scalable and reliable LMS infrastructure, yet institutions often struggle to choose the right cloud platform because decisions rely only on catalog prices or features without empirical performance evidence. This study compares the performance of Amazon Web Services and Google Cloud Platform at the Infrastructure as a Service layer through five stages: provisioning two equivalent virtual machines, deploying Moodle with its database and monitoring stack via Docker containerization, executing JMeter load tests at 100, 250, and 500 concurrent users, collecting performance metrics, and evaluating them with the Analytical Hierarchy Process across four criteria of performance, reliability, cost, and integration. GCP excels in error containment (as low as 0.12%) and OS-level stability and is 27.7% cheaper, while AWS leads in throughput up to 11.7 requests per second with consistent maximum response times. AHP yields scores of 0.768 for AWS and 0.762 for GCP with a consistency ratio of 0.041. The contribution of this research is the first integrated evaluation framework combining empirical JMeter load testing on LMS workloads with multi-criteria AHP decision making, together with a portable Docker-based testing architecture replicable on both platforms.