Here's the link at DPReview: http://www.dpreview.com/reviews/canon-eos-5d-mark-iii/28 When you change it to higher ISO the 5D MkIII sure looks like it has less noise to me. Nicer noise is that the new Nikon phrase for less noise when it applies to Canon cameras?
I downloaded all raws of 600d, 5d2, 5d3 and d800 (ugh! clearly the killer sensor) of all isos, imported them into Lightroom and compared them myself looking at the critical area of the threads in the box on a larger screen.
Up to iso1600 I cannot see any difference, at iso3200 it's small, and at iso6400+ it's noticeable - but then both sensors are so bad that it hardly matters to *me* and my future use for such a body (weddings, mostly with flash, if not lens with f2.8 or better). And when comparing the raw samples, it's no noise reduction and no downsizing, so hardly a real world comparison which will even the differences even further.
"Nicer" noise is my term and describes what 5d3 users reported in the forum - the acutal noise isn't much better, but looks more like film and is more "pleasing" - and looking at iso3200 5d2 vs. 5d3 I'd second to that.