Choosing one as an action and inaction of the other. Integrity Leadership viewed in cold and logical ways. No value judgement involved. Value judgement is extraneous. Definition of leadership does not require adjective.
Leadership is able to influence and motivate others.
Adjective weakens nouns. People bring in value because of spirituality and modernity. There are many people who are willing to accept bad leaders. History is an important factor in teaching us if integrity is critical factor or not and yet look at now the number of leaders who are bad but leading. Examine the concept of integrity.