The primary improvement for me is the lack of an IR field. With the Wii-mote, you are limited in your choice of position while playing as the sensor bar must be able to read your inputs. If you move too far in one direction the system will lose track of your controller. The way it handles requisition of the remote when returning to the IR field is jarring.The problem with the move is drift. This doesn't happen with IR. What's so much better about the move for FPS?
That's really the main thing for me. I ran into this problem constantly with the Wii-mote to the point where I avoid playing certain games as a result of the inconvenience. I'm not someone who can sit in one position for long periods of time so managing the the IR system becomes a frustrating. The Move simply does not suffer from this.
The fact that the Move is not directly tied to a physical point on the controller also allows for an additional layer of tweaking allowing for more comfortable play.
The Wii-mote Plus could likely handle much of this as well but most cursor based shooters insist on using IR which I simply don't enjoy using. I hate the IR sensor bar. It has its pluses but it does not suit me.