The design of coronary stents has evolved significantly over the past two decades. However, they still face the problem of in-stent restenosis, formation of neointima within 12 months of the implant. The biological response after stent implantation depends on various factors including the stent geometry which alters the hemodynamics. This study takes five different coronary stent designs, used in clinical practice, and explores the hemodynamic differences arising due to the difference in their design. Of particular interest is the design of the segments (connectors) that connect two struts. Pulsatile blood flow analysis is performed for each stent, using 3-D computational fluid dynamics (CFD), and various flow features viz. recirculation zones, velocity profiles, wall shear stress (WSS) patterns, and oscillatory shear indices are extracted for comparison. Vessel wall regions with abnormal flow features, particularly low, reverse, and oscillating WSS, are usually more susceptible to restenosis. Unlike previous studies, which have tried to study the effect of design parameters such as strut thickness and strut spacing on hemodynamics, this work investigates the differences in the flow arising purely due to differences in stent-shape, other parameters being similar. Two factors, the length of the connectors in the cross-flow direction and their alignment with the main flow, are found to affect the hemodynamic performance. This study also formulates a design index (varying from 18.81% to 24.91% for stents used in this study) that quantifies the flow features that could affect restenosis rates and which, in future, could be used for optimization studies.