Should "unlawful" enemy combatants be treated differently from a "lawful" enemy combatant?
I assume from your question that you're referring to combatants that are now in custody and, further, that US troops have control over the combatants.
From a practical perspective, when the world looks at how we treat prisoners in our control, we are not judged on the basis of how we distinguish between lawful and unlawful enemy combatants. We are judged on how we conduct ourselves and what kind of power we exercise over people in our control. Even though, as the previous editor has suggested, it is important to ascertain whether combatants are subject to the Geneva Convention accords, the fact is that, in a world of asymmetric warfare, where we are often fighting against people who are opportunists and may have no official sanction for fighting against us, we have to treat all captured combatants identically.
In any kind of war, having what is called the "moral highground" is always an asset, not only because morality is a good thing but also because the exercise of moral behavior is applauded by most reasonable people in the world. To the extent that reasonable people see us treating captured combatants differently, their conclusion wil be that we are not acting in accord with any fixed moral or legal code, and that conclusion will ultimately hurt us either on a political basis or on a practical basis--the ones who will pay for our inconsistency will be US troops in the hands of the enemy.
A country or an individual can never be criticized for acting morally and consistently, and in the case of treatment of prisoners, our conduct has to be based on a moral and ethical constant, which, by definition, cannot vary according to whether combatants are "lawful" or "unlawful."
I would argue that they should.
The reason for this is that the distinction between lawful and unlawful enemy combatants is not one that is simply made unilaterally by the United States. Instead, the distinction is written into the Geneva Conventions. Lawful combatants are ones who are clearly fighters and can be easily distinguished from the civilian population. It is important that only lawful combatants should participate in wars so that there will be less chance of killing innocent people. People who do not follow these rules are putting the lives of others at risk unnecessarily and should be afforded fewer rights than those who do follow the rules.