The NEX F3 should be superior to the 1 J1 in low-light due to its larger sensors. Now you say, you see the opposite but have not mentioned how you determine superior.

The F3 has a much larger pixel count than the J1, so if you look at 100% view, it wont look as good as expect per-pixel. However if you display or print to the same size, the F3 would normally come out on top given the same image brightness.

In you example you have one image darker than the other. This of course makes noise stand out more on the darker image since noise appears as a signal-to-noise ratio. This means that the darker the image, the more noise is apparent.

The two icons are see are for Standard color rendition and Adaptive D-Lighting. This is Nikon's equivalent of Sony's Dynamic Range Optimizer (DRO). If you want the best quality, you need to turns this off on both cameras. What they do is boost the dark parts of the image to make them brighter, but this amplifies noise. Depending on which setting, you get different amplification. In my opinion it also makes most images look worse because it reduces contrast.

Of course letting more light in improves the image quality of any camera and so shooting with a larger aperture is better if that gives you the shot you need. If on one camera you can afford a lens with a brighter aperture that will influence your perception of results.