What is the benefit of using a Mezzaluna Knife over a traditional knife
Advantages


no hand needed to hold the food, therefore safer for children or those lacking knife skills
quicker for those lacking knife skills
no need for gloves when cutting foods that can irritate the skin, like chillies.


Disadvantages


Awkward and dangerous to wash in between the blades for the double-blade version. 
Difficult to store safely
A unitasker really only suited for chopping herbs and spices. The most common items chopped in many cuisines, onion and garlic, would require rough chopping first with a traditional knife, making it hardly worth it.
Inhibits the development of valuable knife skills.