This paper investigates the impact of different unravelings in a monitored system of free fermions. The study considers two random-measurement protocols: quantum-state-diffusion (QSD) and quantum-jump (QJ) unravelings. Both protocols maintain the state in a Slater-determinant form, enabling analysis of large system sizes. The research focuses on the distribution of measurement operators along quantum trajectories, revealing a bifurcation where the distribution changes from unimodal to bimodal. The bifurcation occurs at different measurement strengths for the two unravelings, reflecting their symmetries. The study also examines the scaling of the inverse participation ratio (IPR) of Slater-determinant components, finding a power-law scaling indicative of multifractal behavior. The results show that the system exhibits multifractal properties, with the IPR scaling as $ \sim L^{-\alpha} $, where $ 0 < \alpha < 1 $, indicating anomalous delocalization. The findings suggest that the model is always in an Anderson critical phase, with no sharp localization transition. The study highlights the differences and similarities between the two unravelings, emphasizing the role of measurement strength and symmetry in determining the system's behavior. The results provide insights into the dynamics of entanglement and measurement-induced phase transitions in monitored quantum systems.This paper investigates the impact of different unravelings in a monitored system of free fermions. The study considers two random-measurement protocols: quantum-state-diffusion (QSD) and quantum-jump (QJ) unravelings. Both protocols maintain the state in a Slater-determinant form, enabling analysis of large system sizes. The research focuses on the distribution of measurement operators along quantum trajectories, revealing a bifurcation where the distribution changes from unimodal to bimodal. The bifurcation occurs at different measurement strengths for the two unravelings, reflecting their symmetries. The study also examines the scaling of the inverse participation ratio (IPR) of Slater-determinant components, finding a power-law scaling indicative of multifractal behavior. The results show that the system exhibits multifractal properties, with the IPR scaling as $ \sim L^{-\alpha} $, where $ 0 < \alpha < 1 $, indicating anomalous delocalization. The findings suggest that the model is always in an Anderson critical phase, with no sharp localization transition. The study highlights the differences and similarities between the two unravelings, emphasizing the role of measurement strength and symmetry in determining the system's behavior. The results provide insights into the dynamics of entanglement and measurement-induced phase transitions in monitored quantum systems.