While the main stations of Munich and Augsburg are only 30min from each other by high speed train (costing 20€ each way) or an hour by car, you are unlikely to live and/or work in the respective city centres - which can easily double or triple the commuting time.
Furthermore, while Augsburg is certainly cheaper in terms of accommodation (rents, real estate), it is still part of the rich and expensive "Speckgürtel" (approx. "affluent suburbs") of Munich. You have to move far further to save a considerable amount.