Studied are differences of two approaches targeted to reveal latent variables in binary data. These approaches assume that the observed high dimensional data are driven by a small number of hidden binary sources combined due to Boolean superposition. The first approach is the Boolean matrix factorization (BMF) and the second one is the Boolean factor analysis (BFA). The two BMF methods are used for comparison. First is the M8 method from the BMDP statistical software package and the second one is the method suggested by Belohlavek \& Vychodil. These two are compared to BFA, especially with the Expectation-maximization Boolean Factor Analysis we had developed earlier has, however, been extended with a binarization step developed here. The well-known bars problem and the mushroom dataset are used for revealing the methods' peculiarities. In particular, the reconstruction ability of the computed factors and the information gain as the measure of dimension reduction was under scrutiny. It was shown that BFA slightly loses to BMF in performance when noise-free signals are analyzed. Conversely, BMF loses considerably to BFA when input signals are noisy.