We present results of a series of magnetohydrodynamic (MHD) and hydrodynamic (HD) 2.5 dimensional simulations of the morphology of outflows driven by nested wide-angle winds, i.e., winds that emanate from a central star as well as from an orbiting accretion disk. While our results are broadly relevant to nested-wind systems, we have tuned the parameters of the simulations to touch on issues in both young stellar objects and planetary nebula (PN) studies. In particular, our studies connect to open issues in the early evolution of PNs. We find that nested MHD winds exhibit marked morphological differences from the single MHD wind case along both dimensions of the flow. Nested HD winds, on the other hand, give rise mainly to geometric distortions of an outflow that is topologically similar to the flow arising from a single stellar HD wind. Our MHD results are insensitive to changes in ambient temperature between ionized and un-ionized circumstellar environments. The results are sensitive to the relative mass-loss rates and the relative speeds of the stellar and disk winds. We also present synthetic emission maps of both nested MHD and HD simulations. We find that nested MHD winds show knots of emission appearing on-axis that do not appear in the HD case.