Does 3D Thrust vectoring (TVC) provide improved maneuverability over 2D TVC?
Thrust vectoring allows to control an aircraft when the airflow over its control surfaces has separated. Before thrust vectoring, the range of angles of attack in which an aircraft could be controlled was rather restricted.

With the X-31, it was for the first time possible to control a completely stalled aircraft, which enabled much quicker maneuvering in order to get the nose pointed at an adversary. This was powerfully demonstrated by mock air combats with an F-18. The X-31 used a rather simple arrangement with three paddles at the engine exhaust, and this allowed to create both pitch and yaw moments. This makes it what you call a 3D thrust vectoring aircraft.

Modern thrust vectoring nozzles are round and allow to deflect the thrust by up to 20° in both pitch and yaw, making them also what you call 3D. However, this geometry will scatter radar waves in all directions, which makes it unsuitable for stealth aircraft. Therefore, stealthy designs can use only two straight vanes above and below the jet exhaust, which will create only pitch moments. This is what you call 2D thrust vectoring. When two engines are installed, differential deflection will allow to create limited roll moments, but the powerful side forces which allowed the X-31 to rotate its nose (and radar) quickly into the path of its adversary will no longer be possible.

Stealthy thrust vectoring will still allow to control the aircraft at all angles of attack, but the yaw rates possible with a regular thrust vectoring nozzle are no longer achievable. This, and the structural mass of a rectangular exhaust, are the distinct disadvantages of stealthy nozzle designs.