Now-a-days, e-health and healthcare applications in the internet of things are growing rapidly. These applications are starting from remote monitoring of patient's parameters in home to monitoring patients during his life activities at work, transportation, etc. So we can monitor patients at any place outside of hospitals and clinical settings. By using this technology, we can save lives and reduce the number of emergency visits to hospitals. In contemporary time, there are great progress and opportunities for the internet of things (IoT) related E-health systems. Most IoT e-health platforms consist of three main parts; client nodes (patient or doctor), IoT server and IoT communication messaging protocol. One of E-health systems design over IoT challenge is choosing the most suitable IoT messaging protocol for E-health applications. In this paper, IoT remote patient and e-Health monitoring system was designed for monitoring physiological medical signals of patients based on most two famous IoT messaging protocols, MQTT and CoAP. These medical signals can be include parameters like heart rate signals, electro-cardio graph (ECG), patient temperature, blood pressure, etc. This practical comparison between CoAP and MQTT is to choose most suitable for e-health systems. The proposed approach was evaluated based on most significant protocol parameters like capability, efficiency, communication method and message delay. Practical and simulation results show the performance of the proposed E-health systems over IoT for different network infrastructure with different losses percentages.