Every type of network, be it wired or wireless, will be influenced by several key factors for its efficient functioning. Routing issue, applicable to all types of networks, is one among the several such key factors. Wireless Sensor Networks (WSN) has not been exception to this. Moreover, such issues are very critical due to severe resource constraints like efficient energy utilization, lifetime of network, and drastic environmental conditions in WSNs. Neither hop-by-hop or neither direct reach ability is possible in case of WSNs. In this regard, many routing protocols have been proposed to optimize the efficiency of WSNs amidst of above mentioned severe resource constraints. Out of these, clustering algorithms have gained more importance, in increasing the life time of the WSN, because of their approach in cluster head selection and data aggregation. LEACH (distributed) is the first clustering routing protocol which is proven to be better compared to other such algorithms. This paper elaborately compares two important clustering protocols, namely LEACH and LEACH-C (centralized), using NS2 tool for several chosen scenarios, and analysis of simulation results against chosen performance metrics with latency and network lifetime being major among them. The paper will be concluded by mentioning the observations made from analyses of results about these protocols.