I do not think that you can say a vegan diet is always healthier than all other forms of diets. To my knowledge, you may not even say that the diet is healthy. We know that eating processed food is not good for health. There are several processed food items that belong to the vegan category. This means if you are consuming processed vegan food, you would not be on a healthy diet.
 
On the other hand, consuming unprocessed or least processed food items means that you are following a healthy diet. This is usually not a subjective matter, meaning a thing that varies from person to person. That said, some food items that are healthy for you may not be good for another person’s health. In other words, it depends on what you eat. Consume junk food, and then you might experience some health issue(s) over time.