Interesting phenomena during the Au-assisted chemical beam epitaxy of InAs-InSb nanowire heterostructures have been observed and interpreted within the framework of a theoretical model. An unusual, non-monotonous diameter dependence of the InSb nanowire growth rate is demonstrated experimentally within a range of deposition conditions. Such a behavior is explained by competition between the Gibbs-Thomson effect and different diffusion-induced material fluxes. Theoretical fits to the experimental data obtained at different flux pressures of In and Sb precursors allow us to deduce some important kinetic coefficients. Furthermore, we discuss why the InAs nanowire stem forms in the wurtzite phase while the upper InSb part has a pure zinc blende crystal structure. It is hypothesized that the 30 degrees angular rotation of nanowire when passing from InAs to the InSb part is driven by the lowest surface energy of (1(1) over bar 00) wurtzite and (110) zinc blende facets.