Magnetoresistance in many samples of Dirac semimetals and topological insulators displays nonmonotonic behavior over a wide range of magnetic fields. Here a formula of magnetoconductivity is presented for massless and massive Dirac fermions in Dirac materials due to quantum interference of Dirac fermions in scalar impurity scattering potentials. It reveals a striking crossover from positive to negative magnetoresistivity, uncovering strong competition between weak localization and weak antilocalization in multiple Cooperon channels at different chemical potentials, effective masses, and finite temperatures. This work sheds light on the important role of strong coupling of the conduction and valence bands in the quantum interference transport in topological nontrivial and trivial Dirac materials.