What is the difference in the flavour, if any, between mincing garlic (with a mortar and pestle) and chopping, either finely or coarsely with a knife? Sometimes we feel lazy to mince the garlic so we do use chopped garlic and then wonder which is preferable? 

The flavour of garlic depends on how it is handled. While it is being cooked the way it has been handled can either emphasize or mellow its pungency. A head of unpeeled garlic is odourless because its flavouring agents and the enzyme that triggers their release are held separately within the clove. All cooking techniques that break the cell walls, whether dicing, pressing, chopping or mincing, liberate the garlic’s distinctive flavour and aroma. The more cells that are broken, the more stronger the garlic becomes. So you can control the intensity of flavour by how finely you chop the garlic. 

You as the cook can be in command here. So the main point is that whether you press, mince, or slice garlic, and how long you cook it, determines its punch in cooking.

Cooking is also a factor that comes into play. Slow cooking mellows the garlic’s intensity, as the agents that control its flavours vapourise in the heat. That is why a whole head of garlic gently baked is mellow, rich, and not at all overpowering, while even a single clove that is peeled, minced, and used raw adds strong flavour.