A Parliamentary system has a Prime Minister, his or her party, and loyal opposition. The Executive and Legislative functions are a bit merged. A Branch system, on the other hand, further segregates governmental powers and has an Executive Office, Legislature, and Judiciary.
"Efficiency" and "government" are akin to water and oil. They have nothing to do with each other. What is the benefit of government being efficient? Ramming through social agendas to the dismay of the ousted opposition? Finding quicker ways to enact burdensome laws? Crafting a method to bailout immediately failed industries with taxpayer money?
The function of government is not to be efficient; the function of government is to safeguard rights.
Similarly, Presidents and Prime Ministers are oil and water. Prime ministers may lead the party in power and promote agendas; Presidents, by Constitutional standards, have no such authority since that is the function of the legislature. A president is not supposed to lead a political party, but merely be a member of one.
Regarding political parties, we were never supposed to be limited to two. That has evolved simply because Congress has enacted bylaws to keep 3rd parties restricted. However, without new parties with new people with new ideas, elitist representation evolves; no wonder people are tired of demipulicans and republicrats. Real change has no chance. It's even worse than that. Not only has Congress restricted the number of parties, it has restricted the number of seats in representation. By so doing, congressional districts become odd amalgams of discontiguous voting blocs and true representation, along with true debate, is further diminished.
Having removed those restrictions, Congress would be much more viable, debate would be fruitful, representation would be accurate, and the legislative branch would start doing its job. The Executive Office (President) would return to figurehead status, and as far as legislation's concerned, would only enact or veto acts of Congress, like that office was supposed to.
A Branch system, when operating as designed, would be more effective than a Parliamentary system, if only because Executive and Legislative power is not concentrated in one organ of government. Separating powers and maintaining the system of checks and balances is the best way to safeguard individual rights, which is the function of government.