The three main types of city governments are council-mayor (which can come with a strong mayor or with a weak mayor), council-manager, and commission (though very few cities actually have commission forms of government). Each of these has strengths and weaknesses.
The strength of the commission form of government is that it is very democratic and it allows very close attention to be paid to each aspect of city government. In this form, one commission member is elected to oversee each major aspect of government. That person can give his or her undivided attention to that aspect of government. Its weakness, though, is that there is no central authority.
In the council-mayor system, the strength is that you have an elected central authority. This allows one person to be responsible to the people for the whole city government. The main problem with this system is that you can have a mayor who is elected for his or her political acumen but who is a terrible manager. Such a person can significantly harm the way the city is run.
In the council-manager system, you take care of this problem. The manager is a professional who knows how to run a city. This makes this system efficient. The problem is that it is less democratic because the manager is not elected by the people.
I Know that the three basic types of city government are , the mayor-council plan, the council-manager plan and the commission but i do not know the sterngth and the weakness of each of it.