The manifestation of strongly anisotropic reactivity and interaction potential in the kinetics of diffusion controlled reaction is thoroughly investigated using the method of local analysis (MLA) proposed earlier. The MLA enables one to simplify the problem reducing it to the analysis of the stochastic relative motion of molecules in the vicinity of the reactive orientations. Simple analytical expressions for the reaction rate are derived within the realistic model of reactive hemispheres (MRH) assuming that the reaction occurs upon the overlap of the small reactive hemispheres on the surfaces of molecules. Unlike the conventional model of reactive patches (MRP) the MRH takes into account the "thickness" of the reactive region, which is found to lead to the strong (up to two orders of magnitude) increase of the rate. Within the proposed model of ellipsoidal reactive patch the unified formula for the rate is derived that reproduces the results of both the MRP and the MRH. It is shown that the peculiarities of the local shape of molecules in the vicinity of reactive region manifest themselves fairly strongly. The effects of these peculiarities and as well as the effects of anisotropic potential are discussed.