We present cosmological radiation-hydrodynamic simulations, performed with the code Ramses-RT, of radiatively-driven outflows in a massive quasar host halo at $z=6$. Our simulations include both single- and multi-scattered radiation pressure on dust from a quasar and are compared against simulations performed with thermal feedback. For radiation pressure-driving, we show that there is a critical quasar luminosity above which a galactic outflow is launched, set by the equilibrium of gravitational and radiation forces. While this critical luminosity is unrealistically high in the single-scattering limit for plausible black hole masses, it is in line with a $\approx 3\times 109M\odot$ black hole accreting at its Eddington limit, if infrared (IR) multi-scattering radiation pressure is included. The outflows are fast ($v\gtrsim 1000kms-1$) and strongly mass-loaded with peak mass outflow rates $\approx 103-104M\odot yr-1$, but short-lived (). Outflowing material is multi-phase, though predominantly composed of cool gas, forming via a thermal instability in the shocked swept-up component. Radiation pressure- and thermally-driven outflows both affect their host galaxies significantly, but in different, complementary ways. Thermally-driven outflows couple more efficiently to diffuse halo gas, generating more powerful, hotter and more volume-filling outflows. IR radiation, through its ability to penetrate dense gas via diffusion, is more efficient at ejecting gas from the bulge. The combination of gas ejection through outflows with internal pressurisation by trapped IR radiation leads to a complete shut down of star formation in the bulge. We hence argue that radiation pressure-driven feedback may be an important ingredient in regulating star formation in compact starbursts, especially during the quasar's `obscured' phase.