Stimuli-responsive core shell nanogels display collapse properties which are determined by both the core and the shell. We examine the equilibrium properties and the detailed structural changes during a collapse transition of polymer core shell nanoparticles using Brownian dynamics simulations. Gel particles with randomly distributed cross-linking nodes are created. The influence of the cross-linking degree, core/shell mass ratio, and the strength of the interparticle attractive interaction on the collapse behavior is investigated. Both collapsed core and collapsed shell structures are considered and compared with collapsed homopolymer networks. The transition time was found to be reduced with increasing cross-linking degree and inversely related to the depth of the Lennard-Jones potential. Similar to the kinetics of single chain collapse, there is an initial formation of clusters, in this case near cross-linking nodes, and a subsequent coarsening to form a compact globule. Where the nanogels were collapsed into a compact core, the deformation was found to be essentially symmetric, with a significantly slower relaxation time for the shell units compared to the core collapse transition time. Reducing the core size, the shell units were less affected by the presence of a collapsing core. For the system with a collapsing shell, our simulations reveal in some cases an inversion, with the shell compressing and eventually squeezing out the core units. This effect was more pronounced with decreasing cross-linking degree and core/shell mass ratio.