We study the performance of a Si/LaBr3:Ce Compton camera model for scintimammography, and compare it with a Si/NaI(Tl) model of similar geometry. The GEANT4 simulation toolkit was used to study the behaviour of the cameras at 511 keV. Certain simulation steps, such as the modelling of radionuclide decay times, scintillation photon transport and interactions with photomultipliers, as well as detector dead time corrections were included to make the modelling of the cameras more realistic than previous studies. The Si/LaBr3:Ce Compton camera shows superior efficiency of 2.0×10⁻³ and resolution of 5.3 mm over the Si/NaI(Tl) Compton camera model which has the efficiency of 1.6×10⁻³ and resolution of 6.9 mm at a source-to-scatterer distance of interest, 2.5 cm. A similar result sequence is obtained for two breast tumours of 5 mm diameter embedded in the medial region of an average-size breast phantom of thickness 5 cm. Notably, the signal-to-noise ratios (SNR) obtained for the Si/LaBr3:Ce camera are 9.7 and 3.4 for tumour/background radiation uptakes of 10:1 and 6:1, whereas 6.8 and 2.4 were obtained for the Si/NaI(Tl) camera model for the same tumour/background radiation uptakes respectively. It is therefore envisioned that with lower cost, LaBr3:Ce could replace NaI(Tl) as the Compton camera absorber.