I haven't used a Shig (seriously), but I do own and use a KS, so I'll put my thoughts down about them, or mine, anyways. Come to think of it, I did use one before, as well.
The KS is a simple, utilitarian gyuto, made of a very simple carbon steel, it takes an incredible edge with minimal effort. As Marko stated, its HT is straightforward and solid, but doesn't optimize the edge holding capabilities of the steel (not that white steel is known for this trait, but you get the idea). The handle on my KS is plain as can be and to make matters worse, is a standard D. However, with all of that being said, the lack of anything on this knife makes its positive attributes stick out that much more, and the negatives even become positives, once you become acquainted with your KS.
The obvious positive traits of a KS that jump out at you the first time you handle the knife are:
Profile - it's perfect
Grind - Flattish, but thin (on mine and the one I used before). I've said this before and I'll say it again. I'll take a properly done thin grind that has some sticktion over an overly convexed grind every single time. A "Slab Sided" knife with a nice thin grind on the bottom 2/3s will always release food at the shinogi line. (Not that this is how the KS is done, but I'm explaining my previous statement).
Edge length/Feel - I thought my 240 ran short, because it felt so nimble and the tip was right there, begging to be used. I measured it and was more tha surprised to discover that it's actually a 250.
Taper - nice, gradual, properly done.
Blade Height - to me, this is a plus, but to some it would be a negative. I like shorter gyutos, and I think my KS is 43mm.
Performance - I find the KS cuts and feels exactly how I like a gyuto to do so. It's light, has the ability to fall through food and I could use it all day if I had to.
Now, those pesky negatives that turn to positives.... The reason the boring simple nature of this knife ends up being a good thing is because, you never have to worry about dinging the handle, scratching the blade, or taking too long on the stones, getting frustrated and suddenly doubting your ability to take a simple steel and turning it into a crazy sharp tool. Oh, andit turns out D handles are comfy....
As for Shigs, they seem to be wonderful knives, but I don't like the look of the tip. To me, it's too round and clumsy looking. Of course, I've never read that that's the case, so I could be wrong. Based on looks alone I'd take the profile of a KS, and I can't help but think the tip on one is better than that of a Shig, in use.
Realistically, they're both highly-coveted knives, and I'm sure it's for a reason.