My reason for wanting to move comes more from culture and place than cost of living. That said, I do expect my cost of living to be lower, because my cost of living is artificially high where I live today; I could probably cut it in half by moving domestically in the same state.
Crime is a legitimate concern, but it's highly variable across the vast expanse of Latin America. There are very safe places to live across the region, but you need to do your research.