The short answer is, it depends....
Lets recap on the difference between the two categories:
1- Mechanical - This means you can use tools such as brushes, pumice stones, electronic devices or products that are formulated with abrasives. The coarser and the more aggressive materials are generally used in products meant for the body while options that deliver a more gentle exfoliation are used for face. Pay attention here as some of the coarser grains like large particle size salts, sugars and ground pits, which are used extensively in the industry, can actually cause micro tears in the skin during application.
In my opinion a gentle exfoliant should have no distinct abrasive components for facial application. I know some of us are used to the aggressive nature of the scrubs and subscribe to "no pain no gain" but this is not true when it comes to your face!
2- Chemical - This type exfoliation is often achieved with the use of alpha-hydroxy acids (AHAs) glycolic and lactic acids and/or Beta-hydroxy acids (BHA), such as Salicylic acids. These acids vary in potency and irritancy based on their molecular size and chemical structures. They are frequently used to substantiate anti-aging claims. They are very effective in treating acne, blackheads and Milia (those annoying little white heads).