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Entity Alignment (EA) identifies entities across databases that refer to the same entity. Knowledge graph-based embedding methods have recently dominated EA techniques. Such methods map entities to a low-dimension space and align them based on their similarities. With the corpus of EA methodologies growing rapidly, this paper presents a comprehensive analysis of various existing EA methods, elaborating their applications and limitations. Further, we distinguish the methods based on their underlying algorithms and the information they incorporate to learn entity representations. Based on challenges in industrial datasets, we bring forward $4$ research questions (RQs). These RQs empirically analyse the algorithms from the perspective of \textit{Hubness, Degree distribution, Non-isomorphic neighbourhood,} and \textit{Name bias}. For Hubness, where one entity turns up as the nearest neighbour of many other entities, we define an $h$-score to quantify its effect on the performance of various algorithms. Additionally, we try to level the playing field for algorithms that rely primarily on name-bias existing in the benchmarking open-source datasets by creating a low name bias dataset. We further create an open-source repository for $14$ embedding-based EA methods and present the analysis for invoking further research motivations in the field of EA.