For my sins I used to offer tech support on lab equipment (��ã40k analyzers to very clever people who should know how to use them!), I'd start with the assumption that you're doing it wrong and that both instruments are right, it's just you're doing something wrong.
Even something as simple as assuming that wort shrinks by 4% can induce an error, it's not 4.0%, it's 0.9584 Vs 0.9982, so gravity of boiling wort x 1.0415 = gravity of wort at 20C, just that alone gains 1.5 points.
Then when fermenting alcohol has a density close enough to water to mean that 100% attenuation is going to be within a couple of points of 1.000 and can be ignored unless it's a particularly dry and strong cider for example. But it has a greater effect on refractive index as sugar, so 10 brix (1.040) will drop to 5 brix (1.020) not 2.5 brix (1.010) because that much alcohol adds '2.5brix' (approximately). If you ever do some distillation (i.e. alcohol, water and no sugar) then refractometry works really well, and you use liquid cooled (or peltier effect) Abbe refractometers, which work in the same way as the handheld ones, but are far more accurate.