Human activity recognition (HAR) plays an important role in every spheres of life as it assists in fitness tracking, health monitoring, elderly care, user authentication and management of smart homes. The assistive applications can be implemented on smartphones and wearable watches which are easily accessible and affordable. Now-a-days use of smart phones is ubiquitous, sensor data of diverse physical activities can be easily collected by in-built motion sensors. Many research works are proposed in this area using machine learning techniques including deep neural networks to develop smartphone based applications for human activity recognition. Our objective is to find an effective method from a variety of machine learning including deep learning models for low cost as well as high accuracy activity recognition. To fulfill the objective, a comparative performance study has been done in this work by simulation experiments on five publicly available bench mark data sets. The simulation results show that deep learning models, especially, 2D CNN and BI GRU can be promising candidates for developing smartphone based applications using motion sensor data.