We analyze the sensitivity achievable by the current and near-future water(ice)-Cherenkov atmospheric neutrino experiments in the context of standard three-flavor neutrinos oscillations. In this study, we perform an in-depth analysis of the current shared systematic uncertainties, which arise from the common flux and neutrino-water interactions. We then implement the systematic uncertainties of each experiment and develop the atmospheric neutrino simulations for Super-Kamiokande (SK), with and without neutron-tagging capabilities (SuperK-Gd), IceCube-Upgrade, and ORCA experiments. A careful review of the synergies and features of these experiments is carried out to examine the potential of a joint analysis of these atmospheric neutrino data in resolving the θ23 octant and the neutrino mass ordering. Finally, we assess the capability to constraint θ13 and the CP-violating phase (δCP) in the leptonic sector independently from reactor and accelerator neutrino data.