What difference does it make who my ministers are?

According to the manual:

Depending on their Leadership, Courage and Intelligence attributes, your Ministers may generate positive or negative events. A competent Minister will make your life easier while an incompetent one will force you to fire him or suffer the the consequences of his mistakes.

The in-game description of the Council of Ministers lines up with this too:

If your ministers are stupid, cowardly and all-around bad leaders, expect many gaffes, which will brighten the day of Tropico News Today.

In other words, it's more likely that ministers with higher stats will give foreign leaders impromptu rock concerts, save up for free buildings, and kill entire gangs, yielding nice bonuses; while it's more likely that ministers with lower stats will end up flying their laundry on flag poles, calling Europe a US state, and attacking foreign leaders with forks, resulting in negative effects unless you fire them.