In large-scale cosmological hydrodynamic simulations simplified sub-grid models for gas accretion on to black holes and AGN feedback are commonly used. Such models typically depend on various free parameters, which are not well constrained. We present a new advanced model containing a more detailed description of AGN feedback, where those parameters reflect the results of recent observations. The model takes the dependence of these parameters on the black hole properties into account and describes a continuous transition between the feedback processes acting in the so-called radio-mode and quasar-mode. In addition, we implement a more detailed description of the accretion of gas on to black holes by distinguishing between hot and cold gas accretion. Our new implementations prevent black holes from gaining too much mass, particularly at low redshifts, so that our simulations are successful in reproducing the observed present-day black hole mass function. Our new model also suppresses star formation in massive galaxies slightly more efficiently than many state-of-the-art models. Therefore, the simulations that include our new implementations produce a more realistic population of quiescent and star-forming galaxies compared to recent observations, even if some discrepancies remain. In addition, the baryon conversion efficiencies in our simulation are - except for the high-mass end - consistent with observations presented in the literature over the mass range resolved by our simulations. Finally, we discuss the significant impact of the feedback model on the low-luminous end of the AGN luminosity function.