Looking beyond energy harvesting, metal-halide perovskites offer great opportunities to revolutionise large-area photodetection technologies due to their high absorption coefficients, long diffusion lengths, low trap densities and simple processability. However, successful extraction of photocarriers from perovskites and their conversion to electrical signals remain challenging due to the interdependency of photogain and dark current density. Here we report hybrid hetero-phototransistors by integrating perovskites with organic semiconductor transistor channels to form either "straddling-gap" type-I or "staggered-gap" type-II heterojunctions. Our results show that gradual transforming from type-II to type-I heterojunctions leads to increasing and tuneable photoresponsivity with high photogain. Importantly, with a preferential edge-on molecular orientation, the type-I heterostructure results in efficient photocarrier cycling through the channel. Additionally, we propose the use of a photo-inverter circuitry to assess the phototransistors' functionality and amplification. Our study provides important insights into photocarrier dynamics and can help realise advanced device designs with "on-demand" optoelectronic properties.