Over the past two decades, superconducting gravimeters (SGs) have been a key tool to investigate a number of geophysical processes leading to time-variable gravity changes. As SGs are relative meters, even though they are the most sensitive and stable devices currently available, they need to be accurately calibrated. Each branch of Earth sciences that benefits from high-precision gravity monitoring demands calibration of gravity sensors to accuracy of better than 0.1%. This research deals with a calibration experiment performed at the Strasbourg (France) SG site by means of two FG5 (#206 and #211) absolute gravimeters (AGs) and new-generation spring meters (Scintrex Ltd. Autograv CG-3M and CG5 and Microg-LaCoste gPhone). Our goal is to try to use the newest generation of spring mechanical gravimeters (MGs) for calibrating SGs. We discuss the results in terms of precision and accuracy of the SG calibration by means of different metrological and methodological approaches. With the FG5 #211 we derive scale factors for the SG-GWR C026 located in Strasbourg in agreement with those routinely obtained since 1997 by means of the FG5 #206. This confirms that the estimation of the scale factors is independent of the AG sensor. From a moving-window regression analysis between the synthetic body tides and both the SG and MG gravity records we detect significant fluctuations of the SG scale factors over time due to the instability of the instrumental sensitivity of the MGs. Our main results demonstrate that, owing to the time variability of their sensitivity, the used spring meters, even if well calibrated, cannot be used as a stable reference for SGs. As a result, MGs are not suitable to replace AGs for SG calibration, and we conclude that currently the method using parallel recording with absolute gravity meters is still the most feasible calibration approach for SGs.