The main strength of the commission form of city government was that it was supposed to be more transparent and democratic than the kind of government that cities typically had. In the commission form of government, voters elect city council members who become the heads of specific departments of the city government. In other words, these people have both legislative powers (as city council members) and executive powers (as the heads of government departments). This system would be more democratic (people argued) because people would vote directly for the heads of various departments and it would be more transparent because they would know who was responsible for the various functions of city government.
The main strength of the city manager (or council-manager) form of government is that it relies on a professional to run the city’s departments. In a government that has a city manager, the people elect the city council. The city council then hires a city manager. The city manager is hired based on their professional qualifications and experience. This, we can argue, is better than having the city departments being run by a mayor who is elected based on their ability to get people to vote for them. It is more professional and efficient, in this view, to have the city be run by someone who is trained to run a city rather than by someone who is just a politician.