A simultaneous description of hadronic yields; pion, kaon, and proton spectra; elliptic flows; and femtoscopy scales in the hydrokinetic model of A+A collisions is presented at different centralities for the top BNL Relativistic Heavy Ion Collider (RHIC) and CERN Large Hadron Collider (LHC) 2.76-TeV energies. The initial conditions are based on the Glauber Monte-Carlo simulations. When going from RHIC to LHC energy in the model, the only parameters changed are the normalization of the initial entropy defined by the number of all charged particles in most central collisions, contribution to entropy from binary collisions and baryonic chemical potential. The hydrokinetic model is used in its hybrid version (hHKM), which provides the correct match (at the isochronic hypersurface) of the decaying hadron matter evolution with hadronic ultrarelativistic quantum molecular dynamics cascade. The results are compared with the standard hybrid models where hydrodynamics and hadronic cascade are matching just at the non-space-like hypersurface of chemical freeze-out or on the isochronic hypersurface. The modification of the particle number ratios at LHC caused, in particular, by the particle annihilations at the afterburn stage is also analyzed.