In this work, we investigate the dynamics of electromagnetic precursors, recorded prior to significant earthquakes in Greece. The analysis of these signals is performed using Fisher information, which is a powerful tool for investigating complex and non-stationary signals. Our results point to a decrease of the precursor complexity as the main tectonic event is approaching. The results are compatible to those derived using Tsallis entropy. The sensitivity of Fisher information and Tsallis entropy are compared on the basis of the features of the underlying fracture process which they reveal.