WebAssembly has emerged as a lightweight and portable runtime to execute serverless functions, particularly in heterogeneous and resource-constrained environments such as the Edge Cloud Continuum. However, the performance benefits versus trade-offs remain insufficiently understood. This paper presents Lumos, a performance model and benchmarking tool for characterizing serverless runtimes. Lumos identifies workload, system, and environment-level performance drivers in the Edge-Cloud Continuum. We benchmark state-of-the-art containers and the Wasm runtime in interpreted mode and with ahead-of-time compilation. Our performance characterization shows that AoT-compiled Wasm images are up to 30x smaller and decrease cold-start latency by up to 16% compared to containers, while interpreted Wasm suffers up to 55x higher warm latency and up to 10x I/O-serialization overhead.