Using "click to move" and "interact with target" is extremely advantageous over follwoing and turning, especially since they are not mutually exclusive. You can use both if you feel you need to.

Follow and attack is after the fact attacking. You move to the mob, then spin yourself around and then attack. Interact with target is proactive. You issue your commands to your melee units before you enter battle. It is much more like you are a commander sending them in on a mission.

The main advantage is you know that they will all be in melee range and attacking the target. You also can easily switch to second target without having to issue another follow command. Click target number two, they attack. No need to worry about them facing the wrong direction and having to map buttons to turn them around. This turns them automatically.

There are very few instances where Blizzard allows you to move your units without having to hit the arrow keys or using the mouse directly. This is now one of them and is extremely useful.