The flavors in basil - like any herb - are primarily contained within the cells of the leaf. If you tear it, it tends to come apart between the cells so that less flavor is released (because it stays in the cells). If you cut the leaf, you will break open the cells (some of them, anyway), releasing more flavor. This makes the most difference when you are using the basil raw, as in a tomato salad. In cooked dishes, such as a sauce, it does not make as much of a difference because the cooking gets the flavor out of the cells.

My technique is to wash the basil, pat dry with paper towels, and remove the leaves from the stem. Stack several leaves together and roll into a cylinder, then cut crossways into thin strips. Or do like this fellow here!