We employ hydrodynamical simulations using the moving-mesh code AREPO to investigate the role of energy and momentum input from Active Galactic Nuclei (AGN) in driving large-scale galactic outflows. We start by reproducing analytic solutions for both energy- and momentum-driven outflowing shells in simulations of a spherical isolated dark matter potential with gas in hydrostatic equilibrium and with no radiative cooling. We confirm that for this simplified setup, galactic outflows driven by a momentum input rate of order L_Edd/c can establish an M_BH - sigma relation with slope and normalisation similar to that observed. We show that momentum input at a rate of L_Edd/c is however insufficient to drive efficient outflows once cooling and gas inflows as predicted by cosmological simulations at resolved scales are taken into account. We argue that observed large-scale AGN-driven outflows are instead likely to be energy-driven and show that such outflows can reach momentum fluxes exceeding 10 L_Edd/c within the innermost 10 kpc of the galaxy. The outflows are highly anisotropic, with outflow rates and a velocity structure found to be inadequately described by spherical outflow models. We verify that the hot energy-driven outflowing gas is expected to be strongly affected by metal-line cooling, leading to significant amounts (>10^9 M_sun) of entrained cold gas.