The exact four-body equations of Alt, Grassberger, and Sandhas are solved for neutron-3He and proton-3H scattering in the energy regime above the four-nucleon breakup threshold. Cross sections and spin observables for elastic, transfer, charge-exchange, and breakup reactions are calculated using realistic nucleon-nucleon interaction models, including the one with effective many-nucleon forces due to explicit Δ-isobar excitation. The experimental data are described reasonably well with only few exceptions such as vector analyzing powers.