Black holes (BHs) are believed to be a key ingredient of galaxy formation. However, the galaxy-BH interplay is challenging to study due to the large dynamical range and complex physics involved. As a consequence, hydrodynamical cosmological simulations normally adopt sub-grid models to track the unresolved physical processes, in particular BH accretion; usually the spatial scale where the BH dominates the hydrodynamical processes (the Bondi radius) is unresolved, and an approximate Bondi–Hoyle accretion rate is used to estimate the growth of the BH. By comparing hydrodynamical simulations at different resolutions (300, 30, 3 pc) using a Bondi–Hoyle approximation to sub-parsec runs with non-parametrized accretion, our aim is to probe how well an approximated Bondi accretion is able to capture the BH accretion physics and the subsequent feedback on the galaxy. We analyse an isolated galaxy simulation that includes cooling, star formation, Type Ia and Type II supernovae, BH accretion and active galactic nuclei feedback (radiation pressure, Compton heating/cooling) where mass, momentum and energy are deposited in the interstellar medium through conical winds. We find that on average the approximated Bondi formalism can lead to both over- and underestimations of the BH growth, depending on resolution and on how the variables entering into the Bondi–Hoyle formalism are calculated.