According to the current law, some sitting justices can veto new
appointments to the Supreme Court. The new law will enable the
political majority to appoint new justices against the will of the
sitting justices.
This moves closer to the U.S. status quo (one that is not widely considered to be a good one internationally or among many domestic commentators).
But there are many countries (Poland is one example which I am certain that this has been the case at least until very recently) where appointments to higher judicial offices must be made from the ranks of experienced judges in lower judicial offices, often by internal judicial branch administrators to some extent.
Also, the U.S. has a federal system, and in that system, the vast majority of civil ands criminal litigation is handled by state court systems over which the federal government has no control except through appeals from state supreme courts to the U.S. Supreme Court with 50 states plus highest courts in D.C., Puerto Rico, U.S. territories, and the military justice system all handled by just nine U.S. Supreme Court justices who hear less than 100 cases a year.
Importantly and somewhat relatedly, in the U.S., election administration is mostly a state function with only limited federal law and federal court involvement, so Congress and the President don't have direct control over the institutions that hold the elections for those offices in the way that the Israeli legislature does.
So, control over the Israeli Supreme Court is a much more complete centralization of judicial authority than it would be in the U.S. legal system.
The Supreme Court will be unable to cancel Basic (or 'constitutional')
laws.
If the Supreme Court cancels a law, the parliament can vote to
reinstate the law.
The highest court can't cancel basic law in most countries. Some notable exceptions are the U.K. (because it doesn't have an entrenched basic law), India (in which the Supreme Court has held that some higher principles can trump the constitution), and many Islamic countries (in which Islamic law can override the secular constitution).
This is not allowed in the U.S. federal government where it is very hard to amend the U.S. constitution.
It is allowed in Canada in most but not all circumstances (under "the notwithstanding clause") and in the U.K. under the structure of its "constitution."
Also, keep in mind that in many countries (including the U.K.), personal liberties are entrenched primarily through international, multilateral treaties, which effectively allows basic protections of individual liberties of the kind found in the U.S. Bill of Rights to be abrogated prospectively by withdrawing from the treaty in question, which is nearly equivalent to this situation.
Israel happens to protects individuals mostly through its constitution rather than through multilateral treaties.
Israel is close to the U.K. model:
The Knesset enjoys de jure parliamentary supremacy and can pass any
law by a simple majority, even one that might arguably conflict with a
Basic Laws of Israel, unless the basic law has specific conditions for
its modification. Basic laws that include specific conditions include
the following:
Article 4 of the Basic Law of the Knesset, on the electoral system,
can be amended only by a majority of 61 of the 120 Knesset members.
Article 44, which prevents the amendment of the law by an Emergency
Regulation, can be amended only by a majority of 80 members. A
majority of the Knesset members can amend the Basic Laws on the
government and on freedom of occupation.
So, the ability of parliament to reinstate a provision declared to be invalid isn't a huge change from the status quo in Israel.
Further, it is worth noting that in the U.S. and in many other countries, it is fairly easy to change the constitution with a vote of the legislature and a referendum. And, if a proposal to change the constitution has wide support in the legislature, a referendum to adopt that change is also likely to win that referendum.
The answer from Fizz is also correct in noting that:
purely on paper the US system is even more unbalanced than in
historical reality. There's little [but self-restrain/tradition] that
prevents a political/Congress majority there from packing the Supreme
Court with new members and overturning [constitutionality] decisions
that way.
This has indeed been done several times in U.S. history, and the mere threat that it could be done was one of the main ways that President FDR in U.S. history managed to cause the Lochner era Supreme Court to moderate its decision making.
The power of the Supreme Court to cancel simple laws will be
restrained (exact terms still in the making).
This proposal is too vague to say much about.
Many countries do not allow their primary supreme court to cancel simple laws, reserving that power to a special constitutional court. But, Israel does not have a separate constitutional court, so its Supreme Court serves as both an ordinary Supreme Court and as a constitutional court.
The U.S. does not do this, however, and instead affords the power to cancel unconstitutional ordinary laws to all judges (not just the U.S. Supreme Court).
Currently, Ministers cannot choose legal advisers, and their advice is
considered binding. The new law will enable ministers to hire and fire
advisers as they please, and they can choose not
to listen to them.
Currently, the Cabinet's legal adviser is also the Attorney General
(combined with No. 4, this makes the AG the stongest unelected
official in the government). The new law wants to divide that
position.
In the U.S. federal government, legal advisors for the executive branch are chosen by the head of government (who is also the head of state) for the entire executive branch (i.e. unified), rather than on a department by department basis.
In almost all state governments in the United States, legal advisors for the executive branch (i.e. the Attorneys-General) are unified and separately elected and do not work at the pleasure of the Governor and other executive branch officers.
In the Israeli context, which has a unicameral parliamentary system and a weak President, in which the President and the judiciary are pretty much the only officials formally independent of the Prime Minister, this is a pretty significant change in a way that it would not be in the U.S. or many other countries.