Gamma-ray bursts (GRBs) are classified into long and short categories based on their durations. Broadband studies suggest that these two categories of objects roughly correspond to two different classes of progenitor systems, i.e., compact star mergers (Type I) versus massive star core collapse (Type II). However, the duration criterion sometimes leads to mis-identification of the progenitor systems. We perform a comprehensive multi-wavelength comparative study between duration-defined long GRBs and short GRBs as well as the so-called "consensus" long GRBs and short GRBs (which are believed to be more closely related to the two types of progenitor systems). The parameters we study include two parts: the prompt emission properties including duration (T_90_), spectral peak energy (E_p_), low energy photon index ({alpha}), isotropic {gamma}-ray energy (E_{gamma},iso_), isotropic peak luminosity (L_p,iso_), and the amplitude parameters (f and f_eff_); and the host galaxy properties including stellar mass (M_*_), star formation rate, metallicity ([X/H]), half light radius (R_50_), angular and physical (R_off_) offset of the afterglow from the center of the host galaxy, the normalized offset (r_off_=R_off_/R_50_), and the brightness fraction F_light_. For most parameters, we find interesting overlapping properties between the two populations in both one-dimensional (1D) and 2D distribution plots. The three best parameters for the purpose of classification are T_90_, f_eff_, and F_light_. However, no single parameter alone is good enough to place a particular burst into the right physical category, suggesting the need for multiple criteria for physical classification.