My 2 favorite rifles.
Both are good, but the Kimber is better in almost every way, except price. If you want wood/blue it is a close call. The Winchester is considerably cheaper, but I have yet to see one with wood or checkering that is not below average. The internet rumor is that FN is building the actions and barrels and they are having the stocks done off shore. May or may not be true, but I have not seen a good one yet. I've yet to see a wood Kimber that was not absolutely perfect with much better than average wood and excellent checkering. It depends on how much the better wood is worth to you, and the lighter weight of the Kimber.
Accuracy would be about a tie in my experience, which means above average for either rifle.
I have yet to hear of a Winchesters having problems. I have 3 pre-FN rifles that are flawless and have yet to hear of any problems with the new ones. Some of the early Kimbers did have issues, but as near as I can tell newer production rifles have been fine for some time now.
If you want stainless/synthetic the Kimber wins hands down. The Winchester is only around $150 cheaper and uses a much cheaper Bell and Carlson stock. The Kimber uses a much lighter, stiffer synthetic stock that is every bit the equal to a McMillan Edge which will sell for almost $600 for the stock alone.
I really like both of these rifles, but if I could keep only one the Winchesters would be gone and I would keep the Kimber.