Earlier demonstrations of spintronic functionality on flexible substrates have highlighted the potential for spintronics in flexible electronics applications. However, for device applications, the relationship between global magnetization reversal, as measured by hysteresis, and the local reversal processes of nucleation and growth of magnetic domains need to be understood for magnetic systems on flexible substrates. This study compares the local magnetization reversal behavior of perpendicularly magnetized Pt/CoFeB/Pt and Pt/Co/Pt on rigid and flexible polymeric substrates using magneto-optical Kerr effect magnetometry and microscopy. It is shown that while the magnetic hysteresis is comparable, the local details of the nucleation and field driven reversal are quite different and are attributed to the greater variability of the surface structures of the polymeric substrates, which has implications for consistency in device performance.