Gamma-ray energy spectra were acquired for different sizes of cerium tribromide (CeBr3), cerium-doped lanthanum tribromide (LaBr3:Ce), and thallium-doped sodium iodide (NaI:Tl) detectors. A comparison was conducted of the energy resolution and detection efficiency of these scintillator detectors for different sizes of detectors. The results of this study are consistent with the observation that for each size detector, LaBr3:Ce offers better resolution than either a CeBr3 or NaI:Tl detector of the same size. In addition, CeBr3 and LaBr3:Ce detectors could resolve some closely spaced peaks in the spectra of several radioisotopes that NaI:Tl could not. As the detector size increased, all three detector materials exhibited higher efficiency, albeit with slightly reduced resolution. Significantly, the very low intrinsic activity of CeBr3 is also demonstrated in this study, which, when combined with energy resolution characteristics for a range of detector sizes, could lead to an improved ability to detect special nuclear materials compared to the other detectors.