MinHash and SimHash are the two widely adopted Locality Sensitive Hashing (LSH) algorithms for large-scale data processing applications. Deciding which LSH to use for a particular problem at hand is an important question, which has no clear answer in the existing literature. In this study, we provide a theoretical answer (validated by experiments) that MinHash virtually always outperforms SimHash when the data are binary, as common in practice such as search. The collision probability of MinHash is a function of resemblance similarity (R), while the collision probability of SimHash is a function of cosine similarity (S). To provide a common basis for comparison, we evaluate retrieval results in terms of S for both MinHash and SimHash. This evaluation is valid as we can prove that MinHash is a valid LSH with respect to S, by using a general inequality S 2