Answer
Both cities allow you to live a normal life, but neither can be considered safe without reservations. The risk depends on the area, time, route, and habits. In Montevideo, you are more likely to need to consider phone and bag theft, items left in cars, and differences between neighboring neighborhoods. In Punta del Este, seasonality changes the number of people and the overall atmosphere.
Before renting, visit the address during the day and in the evening, walk the route from the bus stop, and assess the lighting and building entrance. Do not display valuables in public or leave items in the car, and keep your phone and banking apps secure in case of theft.
Compare official statistics and data for a specific area, not the country's overall ranking. For a family, the speed of access to police, medical care, and transportation is also important, especially outside the high season.