We carried out a comparative study on the dynamical properties of the Longer Arm (LA) and the Shorter Arm (SA) of different classes of FR-II radio sources (Broad Line Radio Galaxies (BLRG), Quasars (Q), Narrow Line Radio Galaxies (NLRG) and Low Excitation Radio Galaxies (LERG)) based on self-similar model of time evolution of the radio lobes and hotspot properties of radio sources, using the power-law expression for the dependence of hotspot size \((D_{\mathrm{hs}})\), the advance velocity of the hotspot \((v_{\mathrm{hs}})\) and hotspot luminosity \((P_{\mathrm{L}})\) on the core-lobe length \((D_{\mathrm{L}})\). Using observational values of \(D_{\mathrm{hs}}\), \(P_{\mathrm{L}}\) and \(D_{\mathrm{L}}\) we constrained the exponents of these power-law relations for the LA and SA. We also estimated the hotspot pressure, (\(p_{\mathrm{hs}}\)), cocoon pressure within the lobe (\(p_{\mathrm{cc}}\)), the ratio of the hotspot pressure to the cocoon pressure (\(p_{\mathrm{hc}}\)), the cocoon volume (\(V\mathrm{cc}\)), the energy density within the cocoon (\(u_{\mathrm{cc}}\)), the equipartition magnetic field (\(B_{\mathrm{em}}\)) in the lobe, the particle number density at the hotspot (\(n_{\mathrm{hs}}\)), the external density profile \((\rho _{\mathrm{ext}})\) and the kinetic jet power (\(Q_{\mathrm{jet}}\)) for the LA and the SA. Linear regression analyses indicate a tight correlation between the \(D_{\mathrm{hs}}\) and the \(D_{\mathrm{L}}\) of LA for all classes of radio sources with \(r\sim0.5\mbox{--}0.8\). Similar result was obtained for SA except for that of Q with \(r\sim 0.2\). For \(P_{\mathrm{hs}}\) and \(D_{\mathrm{L}}\) correlation, the result indicates a mild negative correlation that seems stronger for the SA (\(r\sim-0.3\) to −0.6) than LA (\(r\sim-0.2\) to −0.4) for all the different classes of radio sources. Comparing the values of \(\rho_{\mathrm{ext}}\), \(B_{\mathrm{em}}\), \(u_{\mathrm{B}}\), \(p_{\mathrm{hs}}\), \(p_{\mathrm{cc}}\), \(V\mathrm{cc}\), and \(u_{\mathrm{cc}}\) between SA side and LA side, indicate that the SA values of the parameters are higher than those of LA; while \((p_{\mathrm{hs}})\) showed higher values in LA than SA for all the different classes of radio sources. Generally, the hotspot has a larger volume on the LA side than on the SA side except for NLRG, while the hotspot of the SA side contains more particle per unit volume than the LA side for Q, BLRG and LERG. Furthermore, Our results indicate that jet kinetic power is higher on the LA side for Q and NLRG but is smaller on the SA side for LERG, with the jet thrust generally higher on the LA side than o the SA side for all classes of radio sources. Generally, our analysis indicates that environmental factor plays an important role in the dynamics and evolution of double radio sources.