Both have advantages and disadvantages — but the modern GOP lays bare critical flaws in the latter.
In a parliamentary system, the executive has power to make laws, but can be fired at any time.
In a divided powers system, the executive can't be fired except at fixed elections, but must follow the laws of an independent legislature and judiciary.
If political parties start capturing multiple branches and coordinating their actions across them, everything breaks down.
Trump would have been out in 2018.