There isn't a big difference in the 2 mfg's....but a couple of notes:
1. Sigs have a different slide dimension and won't fit most 1911 specific holsters.
2. I think all the Sigs have an external extractor ...some Kimbers do or did at least.....maybe its a big deal to you /maybe not ( to me I prefer the internal extractor ) but its not a deal breaker.
I have a couple of Kimbers ....decent guns / not great (Gold combat stainless II 5" and a Tactical Pro 4" ). Mass produced guns...internal parts aren't great. Tac Pro model had a crummy trigger out of factory - a little creep, and a catch in it before it broke / I threw out all the internals and replace with Wilson Parts.
I do not own a Sig ....but I've fired a variety of their 1911's...all pretty good guns. I might give the edge to Sig in their 1911's - if I was looking for a moderately priced 1911 - between the 2 mfg's.
On a budget ...other guns that should be on your list ....Colt and Springfield. I'm surprised at the new Colts - how good they are / in triggers especially. Springfield has been doing a pretty consistent job for awhile.
In high end 1911's ...Wilson Combat and Ed Brown are #1 and #2 in my view...but you're up to at least $ 2,750 ...and maybe a lot more...