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.
extend this concept to the battlefield. suppose instead of being caught at OHare airport, Padilla had been caught after a shootout in an Afghan cave. what happens then, does he also get the trial you say he deserves? does the army have to mirandize him? does the army have to travel with a criminalist to take evidence against him as they would for any "normal" criminal? do the soldiers at the shootout need to be deposed for his trial? how would he get a fair trial, if these normal procedures that are part of any criminal prosecution in this country, were not followed?
Padilla cannot get a trial by the standards in the civilian justice system. are the foreign wiretaps used admissable? do we have to allow his lawyers to depose the top AQ people we have captured as part of Padilla's defense?
as far as I am concerned, he gave up his citizenship when he became an agent of a foreign power.