Recent use scenarios involving human-robot collaboration have revealed that the robots require elastic joints to safely interact with humans. It is also critical to know applied force/torque (f/t) during the interaction for control and motion planning purposes. In this article, we estimate the external f/t values without using any sensors other than low-cost encoders by exploiting the inherent elastic properties of the joint. For estimation, the following two different approaches are used: model based and model free. In the model-based approach, an extended Kalman filter (EKF) and an external force observer (EFOB) are used considering the dynamical behavior of the system to estimate the interaction force. In the model-free approach, the artificial neural network (ANN) utilizes the data gathered from mechanical systems. In comparative analysis, we have, therefore, considered three different estimation methods, two of which are model based and the remaining one is model free (i.e., data driven). Implementing these estimation algorithms experimentally on a variable stiffness joint, we performed an extensive evaluation of their performances. All methods show similar level of performance in terms of the root-mean-square (RMS) error with 0.0847, 0.0841, and 0.1082 N for the EKF, EFOB, and ANN, respectively. Model-based methods do not require continuous data stream through the experimental set up. On the other hand, the ANN does not need an explicit model of the system; therefore, it may become preferable when the detailed model derivation is not possible.