Semiconductor devices and semiconductor device packages may include at least one first semiconductor die supported on a first side of a substrate. The at least one first semiconductor die may include a first active surface. A second semiconductor die may be supported on a second, opposite side of the substrate. The second semiconductor die may include a second active surface located on a side of the second semiconductor die facing the substrate. The second semiconductor die may be configured to have higher median power consumption than the at least one first semiconductor die during operation. An electronic system incorporating a semiconductor device package is disclosed, as are related methods.