And long reply time (for the second time - I hate keyboard shortcuts when they jump you around the web and suddenly long replies are list!)
For this price range you've a few options including:
Canon 400mm f5.6 L - best image quality you can get at this price bracket and focal length. It doesn't have IS support, but for most wildlife and action photography you'll be wanting 1/500sec at the least anyway to help prevent subject motion blue. A tripod or monopod can also both be used to give support when shooting and negate the need for IS. This lens is often very popular with bird photographers.
Canon 300mm f4 IS L (+1.4TC) - a very good quality 300mm lens which also has the bonus of IS support when using the lens handheld. Combine with a 1.4TC to give a good quality 420mm lens with IS support - not as good as the prime above (and the 20mm difference you won't see in the field) but certainly still very good in its own right
Canon 100-400mm IS L - gives you a very usable image quality at the 400mm end, although you'd ideally want to stop down to f7.1/8 to get a jump up in image quality (no lens is its best wide open and superzooms often need stopping down by one stop or just under to give better results). It has IS and a wide zoom range making it a great generalist lens; however if you're going to get it and sit at the 400mm end the whole time you might as well get one of the primes which will give a higher level of quality
Sigma also have 50-500mm and 150-500mm zoom lenses in this market range; note that whilst they are 500mm lenses the general working distances tend to give around 450mm when tested*. They are about in line with the Canon offering and I think that the 50-500mm is the better of the two sigma, even though it covers a much wider focal length range**
Tamron also has a 200-500mm lens which has been quite overlooked in the past, however a good few are using it now and showing that its a very capable lens and certainly worth considering for this price bracket
On the 70-200mm front I have this to say;
Firstly 70-200mm lenses are great lenses and widely used in a massive range of different photographic areas, they are very versatile and a very good option to have in the bag. They are, however, only 200mm long which means unless you are Steve Irwin good at getting close you are going to end up just too far away to get good shots of most wildlife. The only one I would suggest for wildlife as a wildlife lens (as opposed to being used for landscape/general nature shots and supporting a wildlife lens) is the Canon 70-200mm f2.8 IS L MII which can take a 2*Teleconverter to give a 140-400mm f5.6 IS lens that is pretty much on par with the 100-400mm (the 100-400mm in un-edited test situations tends to have the edge, but after editing its very hard to impossible to tell the two apart). Note also that the 70-200mm f2.8 MII is not only significantly more expensive than the 100-400mm but also a touch heavier when paired with the 2*TC (but not unmanageably so).
The other 70-200mm lenses on the market (including Sigma and Tamron versions) are good quality and worth considering; however they'll all generally take only up to a 1.4TC and a 2*TC is just a bit too much for them to deliver a good quality result.
*focal length is measured when the lens is set to infinity, whilst closer distances can result in focal lengths reducing
** double check this from reviews, I think I'm right but I can't be certain.
