Detectivity is the most important performance metric of any sensor. Detectivity is limited by the sensitivity of a sensor when the probe significantly overwhelms the detector noise. But, when the probe is limited in its power budget, as in sensors on mobile platforms, high sensitivity does not guarantee high detectivity. Here, we demonstrate the trade-off between the detectivity and sensitivity of a plasmonic sensor. Plasmonic sensors are popular for their high sensitivity arising from large local field enhancements. However, their Q-factors are bad resulting in low detectivity for limited power-budget situations. This problem can be alleviated by using an array of plasmonic structures forming a quasi bound state-in-the-continuum (BIC). The plasmonic BIC sensors show higher detectivity but smaller sensitivity. We identify the physics behind this trade-off and experimentally demonstrate antimouse-IgG sensing in a gold nano-disk array-based plasmonic BIC sensor. Moreover, we induce a non-Hermitian system to control the Q factor by changing the non-radiative loss with little effect on the near field. Using this non-Hermitian structure we can break the trade-off effect