You can listen to the oral argument in Boumediene here. Unsurprisingly, the conservatives (well mostly Justice Scalia, actually) went after Seth Waxman (arguing for the detainees) on the constitutional question. Justice Scalia challenged Waxman to name a single precedent in which a non-citizen held outside the sovereign territory of the United States (or England) was entitled to habeas even though no statute so provided. Waxman couldn't do it but there are two reasons why this seems not so damning: 1) As to the U.S., even in Johnson v. Eisentrager, the Supreme Court indicated that location and alienage, standing alone, were not necessarily sufficient to defeat the constitutional claim; and 2) The practice in England, under a regime of parliamentary supremacy, does not translate directly. Furthermore, one could argue, as Judge Rogers did in dissent in the D.C. Circuit, that there is also no case in which a court expressly said the writ would not be available for someone like Boumediene.
Meanwhile, the liberals (mostly Justices Souter and Breyer) went after Solicitor General Paul Clement on the question whether (assuming that there is a constitutional right to habeas here), the DC Circuit review provided by the Detainee Treatment Act (DTA) for combatant status review tribunal (CSRT) determinations is an adequate substitute for habeas. Justice Breyer, in particular, argued that the DTA would not permit a detainee to bring certain kinds of constitutional challenges: e.g., he could not say that indefinite detention---even after a procedurally flawless determination that he was once an enemy combatant---is unconstitutional. Clement seemed to concede that this issue could not be brought before the DC Circuit but argued that there is no habeas right to make such an argument. Justice Kennedy, meanwhile, seemed to think that such an argument COULD be made before the DC Circuit, and thus the statute provides for an adequate substitute. And Justice Ginsburg twice suggested that the right thing to do in the case would be to reverse the DC Circuit by saying there is a constitutional right to habeas but to remand to that court for initial consideration of whether the statute provides an adequate substitute.
Bottom Line: If I had to handicap the outcome, I count 4 votes to affirm on the rationale provided by the DC Circuit (Roberts, Scalia, Thomas, Alito), 3 or 4 votes to say that there is a right to habeas here and that the statutory substitute is inadequate (with Justice Ginsburg possibly voting simply to remand for initial consideration of the adequacy), and one vote controlling the outcome (Kennedy, of course) finding that there is a constitutional right but saying that, at least in the current context, the DC Circuit review could be an adequate substitute. Not that my predictions tend to be very accurate.
Posted by Mike Dorf