Stabilization is somthing that the compositor is obliged to do often (insert here a quip about compositors being unstable). The Tracker node has a perfectly reasonable stabilise function in its Transform tab which will move the tracked data directly into a transform function. So what does a Stabilize node do then?
Stabilize will do as it says on the tin. In order for it to work it will need to be fed tracking data gathered using a Tracker node. It can function using data gathered from a single track, however if rotation and scale atributes are to be considered then at least two tracks will be needed.
The only advantage of using a seperete Stabilize node is that the data from the Tracker can be moderated using the offset parameters of Stabilize.