The best way to display the Ten Commandments is to observe them.
-- Gene Morrissey, letter to Editor of NYT
The main briefs and lower court opinions Ten Commandment cases are found (as usual) on Findlaw's Supreme Court information page. The briefs against the displays [Thomas Van Orden (petitioner) and ACLU (respondent)] are well-written. A couple important issues are the fictional place of the Ten Commandments in our legal history (McCreary County) and the true nature of the display in the "easy" case in Texas (Van Orden).
Likewise, there is a clear precedent to striking down a display that is allegedly neutralized a religious display (again, the place in legal history of the commandments and the Declaration of Independence are not really comparable) only after the fact. [There were three versions, the second clearly speaking of "our Christian nation."] The McCreary County case was also used to raise more complex questions, including if "a new test for Establishment Clause purposes should be set forth by this Court when the government displays or recognizes historical expressions of religion," or more broadly, the question if "the Lemon test should be overruled since the test is unworkable and has fostered excessive confusion in Establishment Clause jurisprudence."
The second question is rather broad given the special nature of the case, so the first one appears more likely to be answered. Linda Greenhouse raises the possibility that the case will be largely limited to its facts, which would seem to be something of a waste of time, since the Court had years to select cases to clarify the matter. The altering of the test seems to have be done sub silento, since Justice O'Connor's "endorsement test" is usually addressed whenever Establishment Clause questions are raised. Various liberal justices are willing to use the test as well, at least in display cases, so maybe that will be done here.
The "historical expression of religion" is one aspect of Justice O'Connor's test, such as the discussion in her concurrence in the Pledge Case, which was of particular concern to the litigants in this case. There is a certain bogus nature to this argument because the controversial "displays" tend to be sectarian (as here), not a truly comprehensive look at our religious history. It is ironical that it is left to challengers to show that the displays portray only certain histories, certain religious traditions. Favoring one version over others is the very definition of establishment, even as here where the Ten Commandments is deemed a "non-sectarian" honoring of God's place in our society (accepting for the sake of argument that this is acceptable).
An honest case can be made in various cases public displays sponsored by the government can have some religious content as a "historical expression of religion." For instance, various cities were originally Spanish missions, and the city seal might recognize this fact with a picture of religious buildings and such. Also, maybe a religious institution has some role in local history, such as the place of religious institutions over time in the caring of New York foster children. And, religion played an important place in history through time, and this might be honored by monuments and such. Compare this to the Texas monument, the sole religious symbol among many monuments in front of a court house, submitted by a fraternal order that could easily be honored in a different way.
A final thought. C-SPAN had some coverage of the cases [oral arguments here] on its American and the Courts program. Some of the participants were associated with religious associations, only underlining how claims that the complaints are "anti-religious" is quite debatable.