  Recently, it has been shown that there exist quantum states for which quantum
correlations dominate over classical correlations. Inspired by this
observation, we investigate the problem of quantum correlations dominance for
two-qubit Bell diagonal states in the Ollivier--Zurek paradigm, using both
entropic and geometric approach to quantification of classical and quantum
correlations. In particular, we estimate numerically the amount of two-qubit
Bell diagonal states for which quantum correlations dominate over classical
correlations, and vice versa. Moreover, we show that in general these two
approaches to quantification of correlations provide ambiguous results.
