The three terms you are asking about don’t refer to the same thing. The term “looks-challenged” used by Daniel S. Hamermesh, author of the book
Beauty Pays: Why Attractive People Are More Successful, is a euphemism for “the ugly” or “the unbeautiful.” It doesn’t refer in any way to people with a physical disability or “the physically disabled,” the legal terminology for which is, as you pointed out, “person with disability.” On the other hand, the term “differently abled” used by that Filipino entertainment personality you cited is the politically correct 1990s euphemism for “the disabled.”
Says the online
Urban Dictionary about the term “differently abled”: “Contrary to what the words may suggest, ‘differently abled’ does NOT mean ‘having different abilities;’ more precisely it means ‘lacking expected abilities.’ Since mental disability is generally associated with much more social stigma than physical disability (and hence is ripe for being described by a ‘sensitive’ PC vocabulary), ‘differently abled’ is most frequently encountered in similar contexts as ‘special.’ With this in mind, persons of non-retarded status should construe the phrase as a deep insult.”
This being the case, I think there’s really no basis for determining which of the three terms—“looks-challenged,” “person with disability, and “differently abled”—is better. They are just euphemisms used by polite society in place of their judgmental, often unpleasant-to-hear equivalents.
