Context: Free core nutation (FCN) can be observed by its associated resonance effects on the forced nutations of the Earth's figure axis, as observed by very long baseline interferometry (VLBI), or on the diurnal tidal waves, retrieved from the time-varying surface gravity recorded by superconducting gravimeters (SG). Aims: In this paper, we study the sensitivity of both techniques to FCN parameters. Methods: We analyze surface gravity data from 15 SG stations and VLBI delays accumulated over the last 24 years. Results: We obtain estimates of the FCN period and quality factor that are consistent for both techniques. The inversion leads to a quality factor centered on ~16 600 with an uncertainty of ~3500 from SG and of ~900 from VLBI, and to a resonant period within [ -423.3, -430.5] days for SG and [ -427.8, -431.4] days for VLBI (3σ interval).