The ability to amplify, translate, and process small ionic potential fluctuations of neural processes directly at the recording site is essential to improve the performance of neural implants. Organic front-end analog electronics are ideal for this application, allowing for minimally invasive amplifiers owing to their tissue-like mechanical properties. Here, we demonstrate fully organic complementary circuits by pairing depletion- and enhancement-mode p- and n-type organic electrochemical transistors (OECTs). With precise geometry tuning and a vertical device architecture, we achieve overlapping output characteristics and integrate them into amplifiers with single neuronal dimensions (20 micrometers). Amplifiers with combined p- and n-OECTs result in voltage-to-voltage amplification with a gain of >30 decibels. We also leverage depletion and enhancement-mode p-OECTs with matching characteristics to demonstrate a differential recording capability with high common mode rejection rate (>60 decibels). Integrating OECT-based front-end amplifiers into a flexible shank form factor enables single-neuron recording in the mouse cortex with on-site filtering and amplification.