Systematic analysis of the planar resistivity, Hall effect, and cotangent of the Hall angle for the electron-doped cuprates reveals underlying Fermi-liquid behavior even deep in the antiferromagnetic part of the phase diagram. The transport scattering rate exhibits a quadratic temperature dependence, and is nearly independent of doping and compound and carrier type (electrons versus holes), and hence is universal. Our analysis moreover indicates that the material-specific resistivity upturn at low temperatures and low doping has the same origin in both electron- and hole-doped cuprates.