Only two republican models have endured as long as the Westminster system. They are the American and the Swiss, and only if you ignore their nineteenth century civil wars.  The Swiss is unusual, reflecting the nation itself. While our founders borrowed the Swiss referendum, no one has tried to import the Swiss system. When the American system has been exported, it has never worked successfully for long, even in France.
The American republic has excellent checks and balances against the abuse of power. But it can be inflexible whenever there is an attempt to bring down a government. There is then the danger of a long paralysis, something unknown in the Westminster system. Remember the attempt to impeach President Nixon.

The other weakness is that all of the American institutions are intensely political, even the courts. There is no institution so above politics as the Crown is in the Westminster system.
This is illustrated by the pardon President Bush recently gave to his associate, “Scooter” Libby.

( For an overview of the case, see the timeline prepared by the Washington Post , 3 July, 2007).  President Bush was not of course the first president to pardon a political  ally.  In the dying days of the Clinton administration, a large number were accorded. On his last day in office, President Clinton granted 140 pardons, some controversial including one to Marc Rich: Barbara Olsen, The Final Days, Regnery Publishing, Washington, 2001, page 121.

The decision to grant a federal pardon in the United States is vested in the President, who acts in his own, absolute discretion. It is not a cabinet decision, and there is no convention about advice being necessary. How different it is under the Crown. A pardon would have to be recommended to the Governor-General, probably as a result of a collective decision in cabinet, rather than an individual decision of the Prime Minister. The Governor-General would need to be assured that he had the power to do this, and that all conditions on the exercise of that power had been fulfilled. Even then, he would be entitled to advise against the pardon if he thought it were inappropriate. There are thus more checks and balances under this system, without making it too rigid.

Seeing the weakness of the American system exposed in the Libby affair, Mr Les MacDonald of  Balmain in New South Wales was moved to write to the Sydney Morning Herald.  His letter was published as the lead letter on 6 July, 2007 under the title  “Abuse of the presidential pardon a miscarriage writ large. “ ( The full version is worth reading.)
“If anything further was needed to convince a reasonable person that the US political and legal systems are irredeemably debauched,” he said, “ it is the farce of presidential pardons. This power was granted to the president to enable the exercise of mercy on those who were regarded to have been failed by the legal system. It has been used, by recent presidents, as a "get out of jail free" card for the most egregious criminals who have inhabited high office in the US.”
“Respect by the citizens for the impartiality of their legal system is fundamental to a functioning democracy. Yet most Americans know that judges throughout the US system are often elected not for their judicial expertise but because of their party affiliation and willingness to do the bidding of powerful local party bosses. They also know that the justice handed out to the rich and powerful is a very different…”

“The Supreme Court has also, in recent presidential elections, supplanted the electorate's voice with its judgments about who should be president.”

“The impression that the system gives to objective observers is that it can, and will, be manipulated to ensure that the result is what those in power want, not what the interests of justice demand.”