The US system is far more dysfunctional — we have the Senate, which ensures that there isn’t an opportunity to conduct a vote along any line!

The real lever of power in congress is the parliamentary process in the Senate.

Yeah, the real difference is that in the US, there is a separate election for president. In the UK, as in many other countries, the party that wins parliament gets to form the government (and determine the prime minister or whatever the title of the de facto head of the executive is). In some countries this is complicated by multiparty systems where coalitions are required, but the general idea of aligning the legislative and executive branches in this way is fairly common.