I've got a couple of each, they are different enough that your particular use should have more bearing on your choice than anything else.
On the Kimber, I like the 3 position M70 safety, that it's already pillared bedded and free floated, and that the trigger puts most after-market triggers to shame, never mind other factory triggers.The 13 3/4" length of pull comes closer to fitting me than most stocks, and it comes with a good recoil pad for calibers that that matters in. The light weight is a plus or a minus depending on your point of view, but I do appreciate that they achieved the light weight of my .338 while still makeing it a 26" barreled, 5 shot, all steel and decent walnut rifle. They cost what they cost, but there's nothing to do to it after the purchase.
The Weatherbys are different, weight is on the high side of average. They are a solid rifle and the stock shape suits me. I would have prefered that they took a pound off the action and put it on the barrel. I also have never forgiven them for free boreing the barrels and likely never will. Triggers aren't any better than OK. In spite of not being in love with the design, and being made uncomfortable by the hype, I still drag one rebarrelled to .300 Win around and it always seems to kill everything its pointed at.