Mobile Health (mHealth) applications (apps) are being widely used to monitor 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. These limitations can be overcome by the integration of mobile and cloud computing (Mobile Cloud Computing (MCC)) that expands mobile devices' capabilities. With the advent of different MCC architectures such as implementation of mobile user-side tools or network-side architectures it is hence important to decide a suitable architecture for mHealth apps. We survey MCC architectures and present a comparative analysis of performance against a resource demanding representative testing scenario in a prototype mHealth app. This work will compare numerically the mobile cloud architectures for a case study mHealth app for Endocrine Hormonal Therapy (EHT) adherence. Experimental results are reported and conclusions are drawn concerning the design of the prototype mHealth app system using the MCC architectures.