Both companies make good guns. I have 2 Kimbers that have been 100% from the get go. I've used freinds SA guns that have also been flawless.
I think that in the $1k price range, Kimber has a slight edge in overall fit and finish. Kimbers triggers are much better, in my experiance. 4-4.5#, very crisp. All the SA triggers I've seen have a lot more creep, and feel gritty and heavy.
SA has the best CS in the business, hands down. Kimber has a spotty reputation in this regard. I'd be hard pressed to buy another Kimber soley on principal; I don't like how they run their business and treat customers after the sale. On the other hand, I don't like the idea of buying a pistol that I know I'll have to send to a smith for a trigger job.
If I was in the market for a $1k 1911, I'd take a serious look at Dan Wesson, they've developed an excellant reputation for putting out a great product, though I have no experiance with them.
Not sure if it matters to you, but Kimber is a US made product, SA is made in Brazil; some of their higher-end guns are assembled in the US.