I'm certainly no 1911 aficionado, and I've never owned a pistol from either company. But when I'm deciding on a handgun nowadays, I always think about the warranty. A gun without a lifetime warranty is never an option for me, because regardless of how good a gun starts, it doesn't always remain that way. Anything mechanical can fail, and I tend to think it WILL fail.
That being said, the Kimber only offers a one year warranty, while Sig offers a lifetime, limited warranty.
I'm not clear on the specifics of what each covers. But one year vs lifetime is a pretty big difference.
Also I've heard Kimber 1911s are pretty hit or miss, and might only come with one magazine. For a gun that expensive, I want at least two mags in the box.