For decades, tissue engineering has been largely guided by the paradigm that engineered tissues require appropriate cell types for a specific application, a scaffold to provide three-dimensional (3D) structure, and soluble factors to stimulate growth and proliferation. While this paradigm has successfully guided the creation of homogeneous, small, or thin de novo structures, native tissues often contain regional structural and cellular differences that tissue engineered models struggle to reproduce. Some of this regional variability results from cellular distances to vasculature, which in turn affects available nutrients and tissue composition. Recently, 3D printing has advanced enough for scientists to create vascular structures of different sizes in a variety of shapes. This technology has the ability to precisely incorporate regional variability into scaffolds, which in turn can influence cellular distribution. Here we use a light-based form of 3D printing to incorporate regional variability into constructs that model possible designs for engineered lung replacements and disease models involving skin. We approach this task by fabricating vascular unit cells featuring vasculature and proximal structures of interest for both of these organs. Additionally, we leverage the design freedoms afforded by 3D printing to improve tissue function by exploring designs that do not appear in native physiology. These unit cells are rigorously assessed for their efficiency, and we evaluate both new and existing metrics to quantify their performance. Finally, we explore these vascular unit cells for their utility as both engineered tissue replacements and disease models. We expect that our results will inform the design of engineered organ replacements and disease models and introduce the idea that engineered tissues do not need to perfectly replicate existing native structures.