On the contrary, the Prime Minister in a Westminster style system has much more power than the President of the USA, because the PM fully controls the legislative agenda.
In the UK, Canada, Australia, and New Zealand, laws that spend public money or raise taxes must be accompanied by a "Royal Recommendation". Since the Monarch of each country with respect to the exercise of the Royal Prerogative has been an automaton since at least 1936 (and for hundreds of years with respect to the UK and its legal predecessors), acting only on the advice of the Prime Minister, this means that the PM has a veto on whether Parliament can even consider most important bills. Ireland and India have similar rules, but have (appointed) Presidents instead of a (heridtary) Queen and (appointed) Governor-General.
This is Section 56 of the Commonwealth of Australia Constitution Act (current version): "A vote, resolution, or proposed law for the appropriation of revenue or moneys shall not be passed unless the purpose of the appropriation has in the same session been recommended by message of the Governor-General to the House in which the proposal originated." The Senate and House of Representatives both have rules and standing orders forbidding the debate of votes, resolutions or proposed laws that may not be passed, and the President or Speaker enforces these assiduously.
Moreover, in all of these countries except the UK, either the Royal Assent can be deferred, or the Proclamation can be deferred, in the event Parliament passes a Bill that the Prime Minister does not want. In the UK, the Royal Assent has been automatic and has not involved the Monarch or the Prime Minister since the early Victorian era; Proclamation is not a feature of the UK system -- an Act of Parliament that receives Royal Assent becomes law immediately (or at a future date fixed in the Act itself). It is pretty clear that if it became necessary, the Prime Minister could constitutionally insist that "the Queen withhold Royal Assent in order to consider the Bill" ("la Reyne s'avisera", is the Norman French formalization), which in practice would mean sending a letter to the Department of Constitutional Affairs and the Clerks of both Houses of Parliament.
This is described in Sections 58 (Royal Aseent) and 60 (Proclamation) of the Australian Constitution.
Finally Section 59 of the Australian Constitution uniquely retains the power of Disallowance (it was abolished with respect to Canada and New Zealand, and never existed in the United Kingdom). (It reads: "The Queen may disallow any law within one year from the Governor-General's assent, and such disallowance on being made known by the Governor-General by speech or message to each of the Houses of the Parliament, or by Proclamation, shall annul the law from the day when the disallowance is so made known.")
In effect, these tools represent a Prime Ministerial veto over legislation, available even if the majority of Parliament supports a bill.
Section 59 might actually be used by the new government. It is normally considered a political mistake to do so, but since the campaign dealt with legislation forced through at the end of the Howard premiership, it is plausible that the new Prime Minister can claim an electoral mandate to exercise the power.
In short, the veto powers of a Westminster-style Prime Minister far exceed those of the President, who must veto or not within a short period of time, and whose veto can be overturned by Parliament.
In the Westminster system, the only remedy for Parliament is to refuse to pass the bills the PM actually wants, or to withhold confidence in the government (by declaration of no confidence, or the defeat of a supply bill), which likely would trigger an election. However in that case it is the PM who decides whether to name a replacement, try to secure confidence with a new set of ministers, or set an election date. The Monarch or Governor is expected to act like an automaton in this regard too.
The only two cases in the past few hundred years where this did not happen (King-Byng and Whitlam-Kerr) led to heavy restrictions on the Crown (King-Byng led to the Statue of Westminster, ultimately; Whitlam-Kerr had a less dramatic aftermath but did result in a revision of the rules of the Senate with respect to blocking supply and the convention that the Governor General serves only during the Queen of Australia's pleasure, and that may be tested ONLY through the Prime Minister) and both led to a more or less disgraced Governor-General. In other words, the Prime Minister always wins, especially if he enjoys a majority in the House of Commons/Representatives.
The last British Monarch who refused to act on the advice of the Prime Minister was beheaded.
The last British Monarch who exercised Royal Prerogative without first securing the formal advice of the Prime Minister was forced to abdicate and leave the country.
Since the Prime Minister typically sits in Parliament, can directly influence the progress of legislation within the rules of the House of which he is a member, and enjoys greater party discipline (usually thanks to selecting even junior members of the Ministry from Parliament), these powers are rarely needed. Cohabitation is unusual in Westminster systems; it is commonplace in the USA.
In fact, the President of the USA is much weaker than most heads of government of systems in which a president is given a personal mandate. In France and Germany, for example, the President (or Chancellor in Germany) has greater influence over the process of legislation both formally (various recommendation systems, and stronger vetos) and through the power of patronage appointments.
The President of the USA has enormous power with respect to firing department heads and members of his Cabinet, but is constrained in the upside of patronage since the Senate must approve of most senior appointments. That approval is occasionally embarrassing to the President (and prospective appointees) and may not always be forthcoming, particularly when the appointment is an overt payback to a former member of Congress for showing loyalty in pursuit of a legislative agenda (e.g. John Ashcroft). No such review exists in the Westminster system, or in France, and the legislature's reviews and confirmations in Germany, Italy and Israel (as examples) are tepid to the point of being pro forma.
In fact, I can think of no area in which the President of the United States is formally more powerful than a Prime Minister in any European state other than Liechtenstein. It's just that the exercise of his or her restricted set of powers can be formidable, since the United States is such a large economic, political and military superpower internationally and domestically, so the President seems much more powerful than other executive heads of government.
*sniff* Wasn't that beautiful? How many places do you know can give you an indepth look into the Australian Federal Constitutional law and parliamentary procedure, comparative and historical analysis with other parliamentary systems AND backed up with examples? All in the one, surprisingly easy to understand (atleast for me) breath?
I want to marry Slashdot.
