We have fabricated AlGaAs/GaAs heterostructure devices in which the conduction channel can be populated with either electrons or holes simply by changing the polarity of a gate bias. The heterostructures are entirely undoped, and carriers are instead induced electrostatically. We use these devices to perform a direct comparison of the scattering mechanisms of two-dimensional (2D) electrons ($mu_textrm{peak}=4times10^6textrm{cm}^2/textrm{Vs}$) and holes ($mu_textrm{peak}=0.8times10^6textrm{cm}^2/textrm{Vs}$) in the same conduction channel with nominally identical disorder potentials. We find significant discrepancies between electron and hole scattering, with the hole mobility being considerably lower than expected from simple theory.