In terms of physical treatment, nothing would change since the US is basically following Geneva Convention standards. As POWs, they can refuse to answer questions other than name, rank and ID, and if tried they must be tried by court martial, but only under the same conditions a US soldier would be tried, and only sentenced and punished in the manner a US soldier would be, and at the end of hostilities they would have to be repatriated. This will be difficult in cases where they no longer hold citizenship anywhere, or are not wanted back home. As unlawful combatants, however, they are not as protected from divulging information as a POW. Refusal to answer questions may get you a charge akin to obstruction of justice. Lying may get you something akin to perjury. You don't automatically get to go home after the war, and can be held for crimes after the war, and your conviction takes a majority, not a unanimous vote. essentially, there isn't much law out there protecting you at all if you are an unlawful combatant.
Our interest in keeping them from being labeled as POWs is for the preservation of the Geneva Convention itself. The Geneva Convention applies to 'lawful combatants,' and because it makes the distinction, it sems clear the convention was not designed for just 'anyone.' It does not cover unlawful combatants.... just people meeting specific requirements.
There is a reason for this; the purpose of the convention was to make this very distinction, so that there would be benefits to nations if they behaved according to the rules of war. Nations which discipline their forces so as to prevent violations of the rules of war, are entitled to having their forces treated as soldiers and POWs if captured. Groups which do not take such responsibilities, and permit and encourage their personnel to act freely and indiscriminently without fear of repercussion, as do terrorists, are not covered.
The Geneva Convention clearly notes the manner in which lawful combatants are to be treated. It makes no demands on the part of unlawful combatants, because no nation at the time of the signing had any interest in encouraging conduct contrary to the rules of war. And if protections were provided to those who used not military tactics, but instead used terrorist tactics (like hiding behind civilians or masquerading as civilians), then the convention would have had the effect of encouraging unlawful tactics.
The Geneva Convention required not just reasonably humane treatment for POWs, but also requires POWs to observe and comply with certain expectations. Among these, prisoners must give their real name, their rank, and whom they serve. They must also respect the authority of their captors and comply with basic instructions and orders, salute those of rank, and if required, captives that are not officers must perform reasonable labor as assigned. Captors in turn must provide for their security, keep captives out of harm's way and away from public ridicule, insure that the IRC gets to meet with the captives, provide medical care as needed, adequate food and quarters, etc.
Neither al-Qeada or Taliban have been forthcoming with accurate identification, not even providing their real names. One of the most fundamental requirements of a POW is to provide the captors with accurate names, rank and ID so that the captors can notify the prisoner's government authorities and families and so that aid packages may be received for each prisoner. Unlike real soldiers expecting POW status, neither al-Qeada nor the Taliban have been cooperative prisoners; some have threatened guards, almost all have lied about their identities, and most have no rank as we know it because their loose structure didn't call for it. Both organizations were trying to maintain deniability for the protection of their leadership. Neirther have a responsible force structure that would be associated with a lawful combatant force. In other words, the leadership remains cloaked and unidentified deliberately, and bears no responsibility for its own people. It lets its people do as they please in their war.
It is in the interest of all nations and parties which abhor terrorism to preserve the Geneva Convention for the protection only of those personnel who behave as disciplined soldiers from responsible states or parties, rather than as terrorists which act irresponsibly. This is neccessary to make terrorism as unpalatable as possible- and to make lawful tactics the norm. We must not blur the distinction betwen terrorism and legitimate warfare.