Auto,
Both are outstanding firearms -- the accuracy, quality, reliability, durability of both are first-rate. However, there are MAJOR differences:
> The Sig is SA/DA, with a decocker
> The Kimber is a traditional SA only 1911A1-type, with safeties but no decocker
> The Sig's DA trigger pull is approximately 10 pounds -- this is your first defensive round
> The Kimber's SA trigger pull is about 4 pounds
> The grips (hand ergonomics) are quite different; the Sig's is somewhat larger
Therefore, since they are both excellent autoloaders, I suggest you try them at a local range. One may have better feel, sight picture, or accuracy for you, which is the obvious "tie breaker".
You can't go wrong with either option.