Just a quick comparison using my favorite imaging-resource.com mannequin series of images. The method was to load all three JPEGs into CS5, then crop the J1 image to 4:3, then downsize the SOny and Nikon images to match. Then crop the eyes out of all three and compare.
No contest. J1 wins, RX100 just behind because of slightly higher clumping in the hair, X10 not even in the contest. Chroma blotching, no hair detail, white balance way off … yuck.
Of course, the X10 would fare better shot the way I recommend, but since no one shoots it that way on test sites, this is a fair comparison. Fuji need to step up their game a bit … the competition has really heated up.