Type 1 diabetes mellitus is one of the most common childhood diseases which, if not carefully mitigated, can pose menacing risks like hyperglycemia and ketoacidosis, ultimately leading to heart disease, kidney failure and other life-threatening complications. In order to reduce these risks, two existing control schemes are implemented with the purpose of simulation-based comparative analysis between linear and nonlinear control strategies. In this regards, H1 is selected as a nonlinear strategy whereas lead-lag compensation is the choice from the class of classical linear strategies. The designed control scheme consists of three main components: a controller, an Insulin Feedback Loop (IFL) and a Safety Mechanism (SM). IFL is designed such that it modifies the loop gain for the reduction of postprandial hypoglycemia risks, and the SM predicts the future glucose levels and acts accordingly by modifying the controller output to reduce the risk of hypoglycemia and hyperglycemia. The comparison of the transient and dynamic performances in terms of rise time, settling time and overshoot of both controllers is analysed. It is observed that the H1 gives a far sturdy response as compared to the lead-lag controller.