I think that the premise of the question presumes that Homer and Auden start out at the same point in their analysis of Achilles. I would submit that I think that both authors embrace a different starting point in their articulation of Achilles. Homer sees Achilles as a god- like warrior. He attributes many of the traits of the divine to the warrior. In doing so, Homer wishes to bring out the idea that Achilles' sense of arete and pure warfighting greatness makes him almost more than what he is. Auden does not begin with the viewpoint of Achilles as in the realm of the divine. He looks at him as a soldier, someone whose purpose is more Modernist in scope. Whereas Homer views Achilles in the Classical warrior sense to a degree that he almost is a divine force in his skill, ability and prowess, Auden purely looks at him as a solider, one whose fundamental purpose is an inevitable march towards death. In this distillation, I think that the fundamental question about the nature of war is revealed. Homer sees a certain poetic beauty in war for it is seen as a defense of honor and a way in which glory can be recorded for the ages while Auden views it as something where death is inevitable and the scale of war only results in the feeding of more dead.
It is from this point where I think that each characterization sets in. It is difficult to argue against Auden's point of view because time has settled in to show war as a brutal experience, one in which the widows, widowers, and orphans are the only absolute. In the modern sense, it is so tough to say that the Classical notion of war of which Homer is a part can be seen as nothing more than brutal savagery where the death count becomes the only sustainable "winner." Auden makes this point repeatedly in the poem with images and references that bring out Achilles as simply a cog in the machinery of death through his participation in war. The "Quite another scene" that Thetis finds is a rendering where the savage nature of war is evident, stripped of its initial claims to glory. The imagery of the solider, of Achilles and soldiers like him, having "died as men before their bodies died" is a resonant image that effectively conveys the modern sensibility of war. This is a divergent image than the Classical notion of warfighting that is embraced in Classical texts like Homer. The "weed choked field" is the only constant in war, something far from the mighty and ornate battlefields of Homer. It is here where I tend to embrace Auden's characterization of Achilles only because of the modern sensibility which impacts how I view war. I think that a Classicist or someone who is able to construct the Classical notion of warfighting would embrace Homer's glorious retelling as representative of how the honorable nature of war is evident. Yet, after experiences like World War I Vietnam or other wars where futility is the only audible chord in the vast barrenness, I think that Auden's depiction of Achilles and the landscape of war probably is more consistent with what war has become.