The grinds on the Kagekiyo are a little more consistent and easier to "break in" when it comes time to thin it. However they are also a little thicker than the Fujiyama.
I've dealt with 1 of each and complained a lot recently about the Konosuke, which was a Blue#2. I think the Konosuke is designed to look good until you get down to the basics of maintenance and actually using it, which involves thinning as you go as part of your sharpening regiment. Sorry, but I think it's a nice-looking knife designed for users who might not know better. As soon as you get beyond touching up the edge you might discover that the grind is a mess and there's no way you can restore the lovely finish you've paid the extra $ for because the shinogi doesn't naturally fit the contours of the blade and its straight appearance, disguised by the nice polish, is machined-on for effect.
It's a cheaper knife that sells well, I suppose, because it's been around a while, sounds reputable, and looks good in photos. The common ebony+blonde ferrule handles dress the blades up further, and I also don't think the overall geometry is very effective because getting up the bevel at the shinogi, where other knives might have been more flush with the rest of the blade face, these end up feeling thick especially at the front part of the blade. Very disappointing and I'm not sure why some people say they are impressed unless these are very inconsistent and sometimes much better.
I'm probably not a fan of the wide, uniform-looking bevel with shinogi design on gyuto, although I do like my Heiji, so you could consider this. I've owned a Gesshin Kagekiyo, though, and found that, although too much is put into looks again - the icky sparkling, slippery, lacquered handle; the polished concave wide bevel that won't look good when you first put it to stones (I don't think people realise) - it was a much more carefully made knife, I thought, with a consistent bevel grind and nice taper. The thickness, in contrast to the Konosuke above, was less and this was good because there wasn't an excess amount of width around the shinogi area. It was thinner and cut better. In my case, thinner isn't really a good thing as I like heftier knives. However, after first dealing with the Kagekiyo the Konosuke seemed a sham.