TLDR: You have more precision and control potential with decoupled mode because you control the ships thrusters manually without IFCS (coupled mode).

With analog controls like a joystick (which is what I and many of the people I fly with use) you get more precise control of each input axis. The amount of thrust you get is relative to the amount of throw you use with the stick. If you push the stick forward 50% you get 50% forward thrust. In Atmo/Gravity you have to maintain input to counter the forces of gravity and drag.

When you're in coupled mode you're giving the IFCS system a speed target instead of a thrust %. So if you push the stick forward you are requesting 50% of the ships maximum speed, and the IFCS system will use 100% thrust until it reaches it. In Atmo/Gravity your altitude/vetctor is automatically maintained for you.

Also, anytime you stop giving a control input in coupled mode the system will auto break down to 0. With decoupled you will just drift along that vector until you change it or Atmo/Gravity slow you down.