You should turn on the optical image stabilization if you think you need it. Optical image stabilization occurs before the image hits the sensor, so you get a full 1920x1080 pixels.
With iMovie's image stabilization, it works by zooming in slightly, so you lose some pixels from your image. If you can imagine each video frame as a rectangle, and then you make a smaller rectangle by including only those pixels that are present in every frame of a scene. That is how, iMovie stabilization works, and it has the effect of zooming in, because the final rectangle is smaller than any individual rectangle.
In general, if you are shooting sports, the best stabilization is to use a tripod. Next best is to use Optical. Third best is to use iMovie. You can use all three at once. You can turn iMovie stabilization on and off very easily once you have analyzed for stabilization, so you can see if it helps you are not.
The reason you see all those warnings about stabilization is that when you apply software (as opposed to optical) image stabilization to a CMOS camera, it can produce a Jello effect where the frame appears to be made of jello. The cameras are better now, so they can control this to a point, but you still may see this effect, which is why they warn you about it. If you have a CCD camera, you will not have this issue. Unfortunately, CCD cameras were more expensive to manufacture than CMOS cameras, so it is rare to find a CCD camera on the market today for consumer level cameras.
