they would have given Padilla his due process - a military tribunal - if the federal courts had kept their hands off this case. it is the courts that have delayed this, and resulted in his 3 year detainment without a trial (a military tribunal is a trial).
what you see now is the endgame - the administration knows they will lose the enemy combatant designation case in the SCOTUS - so they have to try Padilla on charges on which they can actually bring evidence in open court. that's what the request to transfer him to civilian court is all about. the appeals court (led by Luttig) and apparently the SCOTUS want to stick it in their eye and rule on the enemy combatant designation, setting a precedent to disallow its use in the future.
Under the Constitution, US citizens are entitled to a trial by a jury of their peers. A military tribunal doesn't provide this. Such tribunals are part of the executive branch and are not subject to the usual checks and balances.
The Constitution is not, of course, a suicide pact. If we had thousands of US citizen/terrorists one might have to ignore Constitutional guarantees, but my understanding is that this was the one and only US citizen being denied his right to a speedy trial by a jury of his peers. We should not lightly discard our protections against encroachment by government.