The opinions are here; I might have more to say after I read them.
UPDATE: The opinions (six of them) are heavily influenced by the peculiar procedural posture of this case; there’s a lot of talk about standing and about interpretation of an earlier injunction in the case, and the validity of that earlier injunction isn’t squarely before the Court in this particular phase of the litigation. So the Court doesn’t really resolve the enduring uncertainty about the “endorsement test” for the validity of government speech under the Establishment Clause. Justice Breyer doesn’t even clarify his understanding of the proper test, which proved pivotal in the Van Orden v. Perry Texas Ten Commandments case. And Chief Justice Roberts and Justice Alito don’t squarely signal their view on the endorsement test (though their position confirms that they are probably relatively friendly to at least certain kinds of religious speech by the government). The law is still the same mess that it was before.
If I had to label one opinion as most persuasive on the broader questions, I think it’s Justice Alito’s (though I disagree with his reliance on the lopsidedness of the Congressional votes in this case, and on the “country’s religious diversity [being] well represented” in Congress, see the top of p. 6 of his opinion in the PDF file I linked to above). But the case as a whole unfortunately tells us little about the law on those broader questions.