I recently made the move to carrying a Sig 938, which is basically the same gun. The only differences I see are the Sig has a checkered front strap, an external extractor, and nite sights are standard on all their models I believe. Looking at the specs on the two guns there is very little difference. You can even use the Sig mags in the Kimber including the extended 7 rounder but that one has to be slightly modified to lock in.
I really like the Sig. Its very light weight so it carries well, accurate, and runs all ammo very well. I switched to it from a Beretta Nano that I had carried for years mostly because I could shoot the Sig way faster and more accurately from the first time I picked it up. The trigger is a little heavy at about 7.5lb break, but its short, sort of crisp and resets quickly so it doesnt feel that heavy while shooting it.
To make sure I was making a positive change I took both the Nano and 938 to the range, set up a few IDPA targets, got the timer out, and went to it. There was really no contest, the 938 was faster and more accurate everytime. I could hold better groups at 25 yds with the Nano, but that was the only advantage it had.
Look forward to hearing more about the Kimber, hope you enjoy it.