Where there is flexibility in word order, the difference becomes one of emphasis. For example the Subject Verb Object order is strict in English but in other languages where Subject and Object can be distinguished by case, there is greater flexibility in placement, allowing variation for emphasis (e.g. on who did vs to whom).
In your case both are grammatically permissible, so the difference comes down to a bit more weighting on either the hair itself or its relative status. English puts a bit more weight toward what's at front:
I have better hair than him.
I have hair better than him.
As such you'll rarely hear the latter, unless someone is really into their hair.