Justice Kennedy cast the swing vote in a 5-3 decision:
"Trial by military commission raises separation-of-powers concerns of the highest order," Kennedy wrote in his separate opinion. "Concentration of power (in the executive branch) puts personal liberty in peril of arbitrary action by officials, an incursion the Constitution's three-part system is designed to avoid."
Alito sided with Thomas and Scalia. Chief Justice Roberts recused himself because he'd already backed the administration in his previous job as an apellate judge.
This is a major defeat for the administration, but it shows exactly what the president was up to appointing two justices with such an expansive view of presidential power. Bush is one vote away from the Supreme Court signing off on his blank checks.