Mobile Health (mHealth) apps are being widely used to monitor the health of patients with chronic medical conditions with the proliferation and the increasing use of smartphones. Mobile devices have limited computation power and energy supply which may lead to either delayed alarms, shorter battery life or excessive memory usage limiting their ability to execute resource-intensive functionality and inhibit proper medical monitoring. This paper presents a methodology for measurement-based performance assessment of cloud backend and mobile networks that support mHealth services. The methodology targets the assessment of a prototype mHealth app developed for breast cancer patients undergoing Endocrine Hormone Therapy (EHT). It models third-party cloud backend services to examine the performance in a representative testing scenario for end-users accessing the app. Experimental results are reported and compared for native Android and iOS implementations. The analysis further reflects the impact of the network and device battery conditions on response times and end-user quality of experience. The contribution of this work is twofold: (a) First, it presents a performance methodology and analysis of a fully functional medication adherence management mHealth app implemented on major duopoly of mobile platforms (android and iOS) and (b) Second, based on the performance analysis, conclusions are drawn that serve as the recommendation pathway for the development of similar medical reference mobile apps.