I own both, but have not had a chance to shoot the Winchester yet. I have the stainless Kimber and the stainless Winchester Extreme Weather.
The Kimber I bought new about 1.5 years ago and has had no problems. It shoots MOA with my handloads pretty consistently. I forget the exact price, but it was $1,100+ after sales tax. That is about $100 more than a comparable Winchester.
I found the Winchester on consignment in a shop used, but unfired with the box for a little over $800. Have not shot it yet, but I do own one of the Winchester Classics. If it is better than the Classic it will be a great gun.
I think it really comes down to how much you are willing to pay for a lightweight rifle. The Winchester is not really a lightweight. Short actions are 6 3/4 lbs and long actions are 7 lbs. Not bad, but the Kimber Montana is just a hair over 5 lbs. Mine weighs 5 lbs 15 oz. with a Leupold 2.5-8X scope in Talley lightweight mounts. My Winchester should be around 7 lbs. 10oz. with the same scope and mounts.
The synthetic stock on the Kimber is much, much, much better than the synthetic stocks on the Winchesters. While I don't own either in a walnut stock, I'd say the wood is also much better on the wood Kimbers I've seen as well if that is important to you.