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Several three-terminal organic bioelectronic structures have been proposed so far to address the needs for a variety of biosensing applications. The most popular ones utilized organic field-effect transistors operated in an electrolyte, to detect both proteins and genomic analytes. They are endowed with selectivity by immobilizing a layer of bio-recognition elements. These features along with the foreseen low-cost for their production, make them very appealing for point-of-care biomedical applications. However, organic bioelectronic transistors do not always exhibit a performance level beyond state-of-the-art electrochemical sensors, which have been dominating the field for decades. This review offers a perspective view based on a systematic comparison between the potentiometric and amperometric electrochemical sensors and their organic bioelectronic transistor counterparts. The key-relevant aspects of the sensing mechanisms are reviewed for both, and when the mathematical analytical expression is actually available, the amplification factors are reported as the ratio between the response of a rationally designed transistor (or amplifying circuit) and that of a homologous electrochemical sensor. The functional dependence of the bioelectronic sensor responses on the concentration of the species to be detected enabling their correct analytical quantification, is also addressed.