As for the second part in russian superiority comparisons (John is taller than Peter) I see two ways to build it in conflict between them, These are:
1) It can be used equally Р.П. или чем + И.П. "Он выше меня" или "Он выше,чем Я".
2)
2.1. Р.П. can be used when we compare two persons or things from the point of view of a unique quality: Он говорит лучше меня, Он выше меня.
2.2. чем must be used
2.2.1. If comparison refers to two qualities of the same person or thing она скорее полная, чем худая
2.2.2. If the second part of comparison is indeclinable: сешодня иетер сильнее, чем вчера; or if the second part is already determined by a preposition: в Советском Союзе снег идёт (шёл) чаше, чем в Испании.
It is true that the first way (the simplest) I have found in three grammars and the second only in one very good grammar, but I would appreciate your opinion. Thanks.