The influence of shear flow on the phase separation of aqueous poly(N-isopropylacrylamide) (PNiPAM) microgel suspensions was investigated by means of rheo-turbidity and rheo-small angle neutron scattering (rheo-SANS) and compared to the behavior of linear PNiPAM macromolecules. The rheological behavior of concentrated microgel suspensions depends strongly on temperature, but flow and viscoelastic properties of concentrated solutions of the linear polymer are not significantly affected by temperature changes. Shear-induced phase separation was observed for both polymer architectures, although the viscoelastic properties of the two systems have different structural origins. Shear-induced demixing was found with a microgel with a cross-linking density of 1.5 mol % only at high concentrations when the sample behaved as a viscoelastic solid near the equilibrium demixing temperature. No influence of shear flow on the miscibility gap was observed for a PNiPAM microgel with a higher cross-linking density (5.5 mol %). This indicates that a coupling of shear stress with the concentration fluctuations leading to solvent squeezing is only possible when the particles are densely packed and sufficiently soft.