Selection of an appropriate Multiple Attribute Decision Making (MADM) method for providing a solution to a given MADM problem is always challenging endeavour. The challenge is even greater for situations where for a specific MADM problem there exist multiple MADM methods with similar degree of suitability. The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and its dominant variant the Modified TOPSIS methods are two very similar methods applicable to the same type of MADM problems. This study provides extensive simulation-based comparisons and mathematical analysis of these two popular methods in order to clarify the confusion regarding their selection for solving MADM problems.