We study two hybridization algorithms that are used for combining a quantum inertial sensor based on atom interferometry with a classical inertial sensor for onboard acceleration measurements. The first is based on the direct extraction of the interferometer phase and has previously been used in seaborne and airborne gravity-measurement campaigns. The second relies on the combination of three consecutive measurements and was originally developed to increase the measurement range of the quantum sensor beyond its linear regime. After comparing their performances using synthetic data, we implement them on acceleration data collected in a recent airborne campaign and evaluate the bias and scale-factor error of the classical sensor. We, then, extend their scope to the dynamical evaluation of other key measurement parameters (e.g., alignment errors). We demonstrate an improvement in the correlation between the measurements of the two accelerometers, and we observe a significant reduction in the error in the estimation of the bias of the classical sensor.