We present recent JCMT and BIMA array polarimetry data of nearby star-forming regions in order to compare the core and cloud-scale magnetic field geometries in two regions of Orion. The similarity of the magnetic field geometry in these cores to that of their ambient clouds is contrasted with JCMT data toward the Barnard 1 dark cloud in Perseus, which reveal a different magnetic field orientation between the majority of the cores and the surrounding cloud; each of the cores exhibits a different mean polarization position angle. We conclude that the preservation of the magnetic field geometry is better in cores formed within clouds with ordered large scale structures. In Barnard 1, the cores may quickly exhibit a different polarization pattern if they have, for example, rotation which differs from the large scale cloud motions, or a weaker component of ordered fields. This could also explain why the cores exhibit such different geometries from each other in Barnard 1.