The true advantage is that no branch can do it all, if one branch has supreme power such as in monarchies, they will end up doing as they please. When you separate these it makes it unlikely for one group to take complete control of the government. Such as with the American government, the judicial can not do anything that the executive can do, but they can make sure that the executive doesn't just go off abusing power. The legislative gets to make laws, but it must be approved by the executive and the judicial can rule if it's constitutional or not. This is how checks and balances work, this can only happen in a government with separated powers.
