Cosmological constraints derived from galaxy clusters rely on accurate predictions of cluster observable properties, in which feedback from active galactic nuclei (AGN) is a critical component. In order to model the physical effects due to supermassive black holes (SMBH) on cosmological scales, subgrid modelling is required, and a variety of implementations have been developed in the literature. However, theoretical uncertainties due to model and parameter variations are not yet well understood, limiting the predictive power of simulations including AGN feedback. By performing a detailed parameter-sensitivity study in a single cluster using several commonly adopted AGN accretion and feedback models with flash, we quantify the model uncertainties in predictions of cluster integrated properties. We find that quantities that are more sensitive to gas density have larger uncertainties (∼20 per cent for Mgas and a factor of ∼2 for LX at R500), whereas TX, YSZ and YX are more robust (∼10–20 per cent at R500). To make predictions beyond this level of accuracy would require more constraints on the most relevant parameters: the accretion model, mechanical heating efficiency and size of feedback region. By studying the impact of AGN feedback on the scaling relations, we find that an anti-correlation exists between Mgas and TX, which is another reason why YSZ and YX are excellent mass proxies. This anti-correlation also implies that AGN feedback is likely to be an important source of intrinsic scatter in the Mgas–TX and LX–TX relations.