Good question. I just shot these two photos outside. Canon 500D, 18-55mmIS @ 18mm. Both were ISO6400, f18, 1/2500. The only difference is I did one on large fine, the other on medium fine. All other settings (noise reduction) were default.
First up, large fine jpeg:
As you can see, ISO6400 on the 500D is pretty terrible. Next up, more or less the same photo, but using medium fine quality:
As you can see here, the image is quite a bit smaller. As a comparison, I've resized the large jpeg to be the same size as the medium:
this image has slightly more detail, in the bricks for example. It is hard to tell from this particular image.
But long story short, on a pixel by pixel basis, you will get less noise by recording on medium jpeg, but in doing so you are sacrificing image size. Shooting large jpeg and resizing will give you a bit more detail than simply shooting in medium.
Of course, these tests have ignored RAW and subsequent processing with software based noise reduction.
EDIT: Here is almost the same photo, but at ISO100, 1/40, f18. Probably 10 minutes later in the day than the other two, but it gives you an idea.