Recent theoretical and experimental interest has focused on the issue of the dominant scattering mechanism which limits the mobility of the two-dimensional electron gas formed at the molecular- beam-epitaxy (MBE) interface of an A1GaAs/GaAs heterojunction. Measurements have been made at 1.3 K with MBE-grown A1GaAs/GaAs heterojunctions, indicating a difference of nearly an order of magnitude between transport scattering times, expressed as a mobility, measured via either the Hall mobility (classical scattering time) or from the de Haas -Shubnikov oscillation envelope (quan- turn scattering time). This result is contrasted with measurements from the quahtatively different Si metal-oxide-semiconductor field-effect transistor (MOSFET) interface where, over the same charge- density region, the two mobilities are nearly equal and limited by interface roughness scattering.The ratio of the quantum-to-classical scattering time from competing scattering mechanisms is cal- culated. The observed low ratio in the heterostructures is in excellent agreement with the calculated screened-Coulomb scattering from residual charge centers in the A1GaAs, while the lack of this ef- fect in the MOSFET s is in excellent agreement with the surface roughness calculation. The mea- sured scattering-time ratio is thus a new method of directly selecting the dominant scattering mech- anism among competing effects. Stray effects which could interfere with the quantum measure- ments are discussed.