18 USC 4001(a) says the feds can't detain American citizens absent authorization by Congress. The majority and minority opinions agreed that this does not apply to American citizens seized outside the US and then brought home, because the President has that inherent military power under the Constitution. They also agreed that a Congressional resolution can constitute authorization of the Executive branch to detain American citizens seized in America.
They disagreed as to whether the post-9/11 resolution did. I agree with the dissent, which pointedly notes that the 2-judge majority panel admitted that the resolution gave the President full war-time powers against specific non-governmental organizations, one being Al Qaeda. And the Executive branch said Padilla was a pre-9/11 member of Al Qaeda.
The majority opinion basically says that a President's general war powers don't permit detention of American citizens as enemy combatants when they are seized in this country, and that a Congress resolution on the subject must specifically state that it authorizes such detention. The dissent well shreds their reasoning - general war powers are general war powers, period.