Do you have an open jaw ticket flying home from Munich? There are plenty of connections (direct) to Munich, so from that perspective Munich is more attractive to visit, and you can fly home direct from Munich.
Train connection wise, it is slightly a shorter journey to Strasbourg. Not sure what your interests are, but I favour Munich.
Having been to both, I would say that there's more to do in Munich. Strasbourg is a very pretty city and has the European Institutions, but the range of museums and galleries in Munich is better, for my money; plus you have the English Gardens. Neuschwanstein is also a popular day-trip, depending on how much time you have.
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