Advantages of the parliamentarian system over presidential include:

- short campaigns where the parties run, rather than personalities - short campaigns because the PM can call snap elections any time - parliament is usually not adversarial towards the government - elections are less frequent

Disadvantages: - parliament is usually not adversarial towards the govt - elections are less frequent

What I'd like to see is a way for the House of the U.S. Congress, and the POTUS, to be able to do something similar to calling snap elections: accelerate the election schedule by shortening the terms of currently-sitting congress-critters and the POTUS. (Presidential term limits would have to be adjusted to an amount of time rather than number of terms.) I think this would give us the best of both worlds. It would give Congress a huge check on the POTUS and vice-versa: whenever POTUS is very unpopular Congress could call elections, and whenever POTUS is very popular POTUS could call elections. And campaign seasons would be much shorter: presidential campaigns would not be two years long, but weeks or months. But a new primary system would be needed, that's for sure.