I have not yet read the complete opinions, but from what I've seen of not only the Stevens majority, but also the Kennedy and Breyer concurrences (see Orin Kerr with the relevant AMK and SGB excerpts here), it is hard to overstate the principal, powerfully stated themes emanating from the Court, which are (i) that the President's conduct is subject to the limitations of statute and treaty; and (ii) that Congress's enactments are best construed to require compliance with the international laws of armed conflict.
Even more importantly for present purposes, the Court held that Common Article 3 of Geneva aplies as a matter of treaty obligation to the conflict against Al Qaeda. That is the HUGE part of today's ruling. The commissions are the least of it. This basically resolves the debate about interrogation techniques, because Common Article 3 provides that detained persons "shall in all circumstances be treated humanely," and that "[t]o this end," certain specified acts "are and shall remain prohibited at any time and in any place whatsoever"—including "cruel treatment and torture," and "outrages upon personal dignity, in particular humiliating and degrading treatment." This standard, not limited to the restrictions of the due process clause, is much more restrictive than even the McCain Amendment.
My understanding is that this decision technically blocks the President from using military tribunals to try and convict prisoners at Guantanamo Bay, Cuba, though at first glance it also blows the President's "enemy combatant" rationale all to hell, and is a gut punch to the "unitary executive" theory underpinning this outlaw Administration.
Surprise, surprise: Scalia, Thomas, and Alito dissented.