We propose new types of density dependent contact pairing interaction which reproduce pairing gaps in a wide range of nuclear mass table. We discuss also the relation between the proposed paring interactions and the pairing gaps in symmetric and neutron matters obtained by a microscopic treatment based on a bare nucleon-nucleon interaction. It is shown that the isovector type pairing interaction is necessary on top of the isoscalar term to reproduce systematically nuclear empirical pairing gaps. The BCS-BEC crossover of neutrons pairs in symmetric and asymmetric nuclear matters is studied by using these contact interactions. It is shown that the bare and screened pairing interactions lead to different features of the BCS-BEC crossover in symmetric nuclear matter.