Governmental Benefits: British Parliament System vs. System of Checks and Balances

While the British parliament system, existing in countries such as Canada, can differ greatly in regards to the country's dispersal of power in comparison to the United States' system of checks and balances/separation of powers, the two structures of democratic government have fairly equal benefits.
In a parliament system, one of the huge benefits I see is the way their elections run. While the United States and Canada both indirectly elect the leader of their country, it is done much differently. Prime Ministers are selected by the majority party group within the rank of MPs, which are of course chosen by the voters themselves. Because the people do not vote for a prime minister as a way of figuring out the popularity of a candidate, I believe that it helps unify the voters behind their prime minister more so than in America where the case can arise when the electoral college and the voters pick different presidential candidates to win the election.
Still, I feel that the United States has a benefit over these traditionally British systems of government with the separation of powers and the checks and balances system associated with it. A prime minister essentially rules the entire country with little limit to his legislative or executive power. This makes it extremely easy for such a leader to govern his country according to his own, personal agenda. In the United States however, the executive, legislative, and judicial branches are given very separate powers that are limited by the system of checks and balances that forces the branches to work together. No one branch can overpower the other two and completely take over. For example, the judicial branch can declare any presidential act unconstitutional, while the executive branch (the president in this case) can veto congressional legislation and the legislative branch can impeach judges. It is much more difficult for a president govern simply with his own agenda with such a system in place.
Maybe some sort of combination of these two benefits found in different structures of government could benefit our country if enacted together.