Modern charge-coupled-device (CCD) detectors can achieve peak quantum efficiencies of 90%, compared with less than 10% for the photocathode of an electron multiplier. We report on laboratory tests of examples of these two detector technologies to evaluate their relative performance for precision Doppler spectroscopy of laboratory plasmas. The tests reveal that the accuracy of the Doppler width and shift measurements improves with the square root of the photoelectron flux, and thus as the square root of the detector quantum efficiency. An analytic estimate of the performance of these two types of detectors confirms the square root dependence on photoelectron flux but also highlights the importance of other noise sources that could be important under different conditions. The gain of the electron multiplier system can be reduced to the level of 10 photon-electrons per ADC count before there is any reduction in the accuracy of the estimation of fitted parameters.