I found some underside images on Wiggle, for the narrow and S. They didn't have underside images for the standard normal. I scaled them to match and superimposed them. The S image isn't exactly straight / perpendicular to the saddle, it is slightly tilted so I stretched it a little bit lengthwise. The superimposed image is probably similar in size to the the standard normal, with a slightly wider middle section by a few milimeters.

From what I could tell, the difference in rail length between the S and narrow is maybe only 6-10mm. The rail looks really short compared to the Flyer.

The metal frame under the rear is really much narrower on the narrow. I wonder if you'd have less leeway in where you can sit before you start feeling the metal underneath.

The punchout in the center is also shorter on the S, by almost the same amount as the difference in length. I suspect the middle-front will feel harder because of that, but whether it has any effect would depend on whether there is a different in lengthwise curvature. I theorize that a shorter length means less hammock.