Objective. Full-field digital mammography (FFDM) systems manufactured by Hologic that utilise either a 2D or linear anti-scatter grid have recently been installed in our clinic. The manufacturer advise that for matched dose, both grids deliver comparable image quality. The aim of this study was to test the manufacturer’s claim using advanced physical image quality metrics and to inform whether the different grids are indeed dose neutral. Approach. Effective detective quantum efficiency (eDQE), effective noise equivalent quanta (eNEQ) and effective dose efficiency (eDE) were measured on a Hologic Dimensions (2D grid) and a Hologic 3Dimensions (linear grid) FFDM system, both calibrated at installation to provide matched threshold contrast, according to the EUREF protocol. eDQE, eNEQ and eDE were calculated and compared using 2, 4, 6 and 7 cm thicknesses of poly (methyl methacrylate) (PMMA) to simulate a clinically appropriate range of breast thicknesses. The beam qualities (target/filter and kilovoltage) chosen were identical between the two systems. Main results. All image quality metrics investigated show that the 2D grid outperforms the linear grid across all spatial frequencies. Furthermore, mean glandular dose (MGD) must be increased by up to 38% on those units that utilise the linear grid if eNEQ is to be matched, although MGD to the standard breast remains within NHSBSP tolerance and below the UK diagnostic reference level. The gradient and shape of each curve was the same irrespective of which grid was used, suggesting that subtle lesions (low frequency information) and micro-calcifications (high frequency information) will be imaged just as efficiently with a linear or 2D grid. Significance. If image quality is to be matched between those units utilising 2D and linear grids, dose must be increased on the latter. This information will be useful to the medical physicist tasked with the optimisation and standardisation of Hologic FFDM units.