The intrinsic relaxation rates of the vector magnetization of cesium vapor enclosed in microfabricated atomic magnetometer cells are investigated. Two methods - the optically detected magnetic resonance (ODMR) and the ground-state Hanle effect (GSHE) - are used to carry out automated measurements in dependence on cell temperature and nitrogen buffer gas pressure. The experimental results are compared to expected contributions of the different relaxation processes and in this way allow the discrimination between them to help further optimization of cell design. The methods are compared in terms of basic features, data quality and practical applicability.