Yes, there are pro’s and con’s for various systems.
The practically free-reign USA system with a 2-year window can lead to a lot more need to actually tailor policies to what the people want, rather than imposed form above. In its best, it produces compromise; at worst, as we have seen, grandstanding and gridlock.
The whipped system (Canada, Britain) with FPTP produces majorities and occasional minorities. The only limit on a majority government’s power is backbench revolt (think Margaret Thatcher) when the policies might take the party so far out of public approval that the MPs all fear for their jobs next election.
In this, I strongly approve of the British system. When you add up all the cabinet ministers, secretaries, and committee heads, that’s about 100 members. add in about 20 to 40 still trying to get noticed and promoted. A majority in Canada is 155 seats, that leaves about 20 or 30 who know they haven’t a hope in hell of getting promoted and so are willing to buck the party leader. (However, these are usually not the best and brightest). Pierre Trudeau famously said “backbenchers are nobodies 100 yards from Parliament Hill.” DO the same math in the 600-seat British system and a majority has 150 to 300 MPs who have to be pleased by the Prime Minister. If the majority is close or a lot of these are upset, they can usually force change. In Canada, this is very rare.
A coalition like the US congress, can be either an opportunity for compromise or a chance for gridlock. Nobody wants a repeat election in less than a year, so “who caused it” is the number one question if the parties can’t compromise. Generally, the third party has to hold their nose and support the government unless they want an election, in which case the government has to decide if they want to play chicken or give it. Ah, politics.
A run-off (France) or Australian system simply gives voters a way to express a preference, or send a message. If there are 2 parties of the left or right, it is possible that likeminded voters can send the message to an errant party, while still choosing them if the other party does not do well. Canada does not have this system, and in 3-way races you often hear “A vote for the NDP is a vote for the Conservatives, because it is one less for the Liberal”.
Proportional representation is the worst of all worlds. It encourages small single-focus parties; it encourages them not to compromise since their single point of view is all that their voters choose them for. The members of parliament are chosen from a list, and the issue is not to appease voters, but to wheedle the party bosses to be as high up that list as possible. You get the gridlock and the main parties “buy” the support of enough small parties to keep in power. Nothing of substance can be done if one of the tiny parties in the coalition rejects it. The ultimate example is Israel, where they are building a Jewsih homeland - yet the supposedly devout but large number of Haredim are allowed to live on welfare doing nothing but studying their religion, and exempt from military service(!) thanks to the demands of fundamentalist religious parties.