I cant help but feel a prime minister system is more stable and less prone to authoritarianism & disenfranchisement than a presidential, winner take all system. Of course the latter is all I've ever known so it's hard to say. The US president is simply too unrepresentative of the people (or, can be) to wield the amount of power the office has.
(Sorry - long response, because it's a complicated issue!)
I don't know about that. There are a number of variations in the "prime minister system". I can't claim to understand how they all work. In many countries there is a president as well as a prime minister & the power of each varies depending on how the system works. In some cases, like Israel or Germany, the president is a mostly ceremonial role & power is invested in the prime minister, in other cases, like, Russia, the president holds more power than the prime minister. In France, both the prime minster & president hold significant power.
The system I am most familiar with is in the UK, & in Canada (which is more or less the same as in the UK). The citizens don't vote directly for the prime minster - the prime minister is the leader of the party that wins the most seats in the parliamentary elections. If the party wins a clear majority of seats, the prime minister is in a strong position to wield total power, as he/she controls both the executive & legislative branches. However he/she must continue to keep the support of the members of parliament from his/her party. Periodically, when the prime minister loses popular support, the party may vote to remove him/her from the position of "prime" minister in order to try & regain popular support for the party. This is what happened to Margaret Thatcher in 1990 - she became personally unpopular in the country, lost the backing of the majority of Conservative MPs & was forced to resign.
Sometimes prime ministers have to form a government without majority support in parliament - this is called a minority government. It obliges the government to rule with the support of one (or more) of the other parties. That is currently the situation in Canada where the Trudeau government remains in power with the (conditional) support of the New Democratic Party. In countries with proportional representation, it is usual for the the prime minister to rule in minority governments - that is the situation in Germany, & most notably in Italy & Israel. The prime ministers in those countries often have an extremely tenuous grip on power, as they must keep a diverse group of parties satisfied in order to stay in power.
The US system is carefully designed to balance the different functions of government. However, as we have discussed, the undemocratic nature of the senate (& the electoral college) makes the system unbalanced in other important ways (IMO). Also, it seems that, for a variety of reasons, the presidency has been taking on more power over the last few decades & Donald Trump, with the acquiescence of the Republican senate, seems to have taken that to a whole new level.
I have noted that (IMO) the system works well in Canada. This is partly an accident of history & circumstances. Unlike the UK, Canada is a federal system with power shared between the federal & provincial governments. Very frequently, changes at the federal level lead to a counter-balancing change at the provincial level. I have observed this happen many times over the last 40 years. Also, Canada has had (at least) 4 major political parties at the federal level. The shifts in voter sentiment can be expressed in a more complex realignment of parliamentary seats & therefore political power, than seems to take place in the UK. In the last 40 years the two major parties: the Conservatives & Liberals, have each been eviscerated at the polls a couple of times & have been forced to re-evaluate & rebuild.
Aside from that, the general tone of political debate is far less adversarial & divisive in Canada & I think there is a much stronger sense of "shared values" than in the US. There is a sense that the parliamentary government should govern by "consent", rather than with the exercise of raw political power. I think that comes partly from the understanding that "the system" itself is not perfect. In contrast, I get the sense that in the US people are so convinced that the system itself is perfect - a product of unequalled brilliance on the part of the Founding Fathers - that it's permissible to game the system for whatever is possible ... which is how we've got to the present state of affairs (IMO).