I've had caribou approach to within 20 yards, and I've seen them spook at ranges of 250 yards. I think it all depends on how experienced the lead animal is. A lot of times I think they're spooky because they've been hit hard by wolves and are just jumpy.
All in all though, they're not a tough animal to hunt, it's just that the terrain they live in can be incredibly tough. Most tundra is basically a swamp interspersed with knee high tussocks that can break your leg if you're not careful. Packing out meat can be incredibly difficult.
Probably the best caribou hunting on earth right now, is the Mulchatna herd in Alaska. This particular herd is on average the largest caribou on earth, both in body weight and antler size. And to put the frosting on the cake, it has enjoyed a tremendous growth spurt over the last dozen years and they now number somewhere in the neighborhood of 300,000 animals.
A good mulchatna bull can top 600 pounds, which is approaching elk size... however..., in my experience, a caribou tends to go down a lot easier than an elk, so you don't really need a heavy rifle.
You can access the Mulchatna herd by chartering out of the Anchorage area which means it's relatively inexpensive to hunt them. Buyer beware when looking for air charters. There are a number of outfits in Anchorage who will do nothing more than dump you on the first big lake across the range, whether caribou are in the area or not. Avoid the larger outfits and ask for references!
If the name "Whitefish Lake" comes up in your conversation, hang up the phone immediately! Whitefish Lake is the first large lake just over the range and several outfits run a shell game where they dump hundreds of hunters into the area and ferry them back and forth.
For the money you're paying, look for an outfit that will put you on a lake of your own (there's a 1/4 million lakes in SW Alaska) AND that will give you some kind of scout flight around the area so you can see there are caribou moving through. Caribou are herd animals and you either see them in hundreds/thousands or not at all.
Keith