Optical Image Stabilization vs Electronic Image Stabilization
Optical Image Stabilzation (OIS) inertially manipulates a prism to stabilize the video image.
Electronic Image Stabilization (EIS) performs transformations on the image. There is no known way to do these transformations without causing at least some image degradation.
So is the degradation of the video noticeable? It depends on how carefully you look and what type of motion is being corrected for. EIS will always degrade the image. If you pause the frame and look at high contrast areas during motion you'll see aliasing and contast loss. Some "Golden eyed" viewers will see it clearly on normal playback. Most normal viewers will not notice any but the grossest errors.
It depends on the situation. If you are correcting small infrequent jitters, there is no noticeable difference. As an example both show the same results whenever called on to eliminate the type of jitters you get when touching or bumping a camera on a tripod.
If you have high frequency motion or if the motion covers a large range of motion optical image stabilization becomes noticeably superior. For example if you are running, or even walking fast, the number of errors that have to be corrected cause EIS systems to produce more noticeable errors in the image. OIS has a better image under these circumstances.
The trade off in a pure OIS system is that it can't correct for motion beyond the ability of the prism to move. In a situation like running, (and I do mean running) OIS will give you smooth motion, where as EIS will give you less motion but greater digital artifacts.
Another sort of artifact OIS delivers is when you have a long slow move, like a pan, the prism keeps moving after you stop, causing the very motion you are trying to eliminate. EIS typically is capable of faster reaction times, and while still susceptible to this effect, minimizes the time it appears.
If you are selecting a camera based on it ability to stabilize images you have to consider the type of motion you intend the camera to correct for. If you expect the camera to recieve frequent high frequency shocks, like being buffeted by wind on vehicle mounts...EIS may be a better choice. If you have lower frequency higher amplitude motion, like walking or whip pans to compensate for OIS may prove superior.
If you are planning on running or the like you can just forget it right off. Look at camera stabilization systems like Steadicam or Glidecam.
Of interest are systems that combine these technologies. The Sony VX2000 has an excellent example of this with its Optical Super Steady Shot.