Exceptional-point (EP) sensors are known for their square-root resonant frequency bifurcation in response to external perturbations, which has led to suggestions for their use in sensing applications. However, there is debate about whether this sensitivity advantage is negated by additional noise in the system. This study shows that the imprecision of an EP sensor in measuring a generalized force is independent of its operating point's proximity to the EP. This is because fundamental frequency noises, due to quantum and thermal fluctuations, increase in a manner that exactly cancels the benefit of increased resonant frequency sensitivity near the EP. Thus, the benefit of EP sensors is limited to the regime where sensing is limited by technical noises. The study outlines an EP sensor with phase-sensitive gain that does have an advantage even if limited by fundamental noises. The paper discusses the behavior of EP sensors, focusing on their sensitivity and noise characteristics. It shows that for PT-symmetric EP sensors, the frequency noise increases as we approach the EP, leading to increased quantum and thermal noise near the EP. This nullifies any improvement in signal-to-noise ratio. However, PT-symmetric EP sensors can offer advantages when limited by technical noises, not fundamental noises. The study also considers non-Markovian dynamics and quantum-enhanced EP sensors, showing that phase-sensitive amplification can recover any advantage lost due to proximity to the EP. The conclusion is that PT-symmetric EP sensors do not offer a fundamental advantage for parameter estimation or weak-force sensing when limited by fundamental noises, but they can offer advantages when limited by technical noises. The study outlines a phase-sensitive generalization of an EP sensor that does confer an advantage by harnessing the square-root bifurcation near an EP.Exceptional-point (EP) sensors are known for their square-root resonant frequency bifurcation in response to external perturbations, which has led to suggestions for their use in sensing applications. However, there is debate about whether this sensitivity advantage is negated by additional noise in the system. This study shows that the imprecision of an EP sensor in measuring a generalized force is independent of its operating point's proximity to the EP. This is because fundamental frequency noises, due to quantum and thermal fluctuations, increase in a manner that exactly cancels the benefit of increased resonant frequency sensitivity near the EP. Thus, the benefit of EP sensors is limited to the regime where sensing is limited by technical noises. The study outlines an EP sensor with phase-sensitive gain that does have an advantage even if limited by fundamental noises. The paper discusses the behavior of EP sensors, focusing on their sensitivity and noise characteristics. It shows that for PT-symmetric EP sensors, the frequency noise increases as we approach the EP, leading to increased quantum and thermal noise near the EP. This nullifies any improvement in signal-to-noise ratio. However, PT-symmetric EP sensors can offer advantages when limited by technical noises, not fundamental noises. The study also considers non-Markovian dynamics and quantum-enhanced EP sensors, showing that phase-sensitive amplification can recover any advantage lost due to proximity to the EP. The conclusion is that PT-symmetric EP sensors do not offer a fundamental advantage for parameter estimation or weak-force sensing when limited by fundamental noises, but they can offer advantages when limited by technical noises. The study outlines a phase-sensitive generalization of an EP sensor that does confer an advantage by harnessing the square-root bifurcation near an EP.