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Quantum states of light can enable sensing configurations with sensitivitiesbeyond the shot-noise limit (SNL). In order to better take advantage ofavailable quantum resources and obtain the maximum possible sensitivity, it isnecessary to determine fundamental sensitivity limits for different possibleconfigurations for a given sensing system. Here, due to their wideapplicability, we focus on optical resonance sensors, which detect a change ina parameter of interest through a resonance shift. We compare their fundamentalsensitivity limits set by the quantum Cram\'er-Rao bound (QCRB) based on theestimation of changes in transmission or phase of a probing bright two-modesqueezed state (bTMSS) of light. We show that the fundamental sensitivityresults from an interplay between the QCRB and the transfer function of thesystem. As a result, for a resonance sensor with a Lorentzian lineshape aphase-based scheme outperforms a transmission-based one for most of theparameter space; however, this is not the case for lineshapes with steeperslopes, such as higher order Butterworth lineshapes. Furthermore, such aninterplay results in conditions under which the phase-based scheme provides ahigher sensitivity than the transmission-based one but a smaller degree ofquantum enhancement. We also study the effect of losses external to the sensoron the degree of quantum enhancement and show that for certain conditionsprobing with a classical state can provide a higher sensitivity than probingwith a bTMSS. Finally, we discuss detection schemes, namely optimizedintensity-difference and optimized homodyne detection, that can achieve thefundamental sensitivity limits even in the presence of external losses.

Fundamental Sensitivity Bounds for Quantum Enhanced Optical Resonance Sensors Based on Transmission and Phase Estimation