Answer:  

Dr. Richard Bojar kindly answered the question above. 
  
  
Depends what you mean by cleaner. The removal of grease and dirt is a function of the soap content, which also has some antimicrobial activity. 
  
Additional agents added to medicated soaps and cleansers are included to enhance antimicrobial activity and, for the most part, they are quite effective. However, whilst it is good to remove contaminating microorganisms from the skin surface, skin also carries a large resident microflora which contributes to skin health, just like the gut microflora keeps the gut healthy. 
  
The available evidence shows that the resident microflora is fairly resistant to normal washing, but there is the danger that excessive or obsessive washing can be detrimental to skin health. 
  
  
Acknowledgement 
Dr. Richard Bojar 
He is studying the physiology and molecular biology of skin microorganisms at the Skin Research Centre (University of Leeds). Please look at the website links for his studies in detail.