We have studied transport properties of nanopillars with high-quality MgO tunnel barriers and with a range of MgO barrier thickness, and compared the bias-voltage dependence of tunneling magnetoresistance, differential conductivity, and resistance in parallel and antiparallel states with theoretical models. The differential conductance in the antiparallel state suggests that the dominant scattering mechanism for this state is inelastic scattering that mixes propagating Δ5 states in the electrode with evanescent Δ1 states in the MgO barrier. In addition, we observed in large populations of parts with both low- and high-voltage bias transport anomalies in the parallel state. Finally, in the junctions studied here, we observed a much weaker decrease in the tunneling magnetoresistance with bias voltage than reported in previous studies. [ABSTRACT FROM AUTHOR]