Looking for a good telephoto zoom lens from Canon, I consider :
- Canon EF 100-400mm f/4,5-5,6L IS USM
- Canon EF 70-300mm f/4-5.6L IS USM
- Canon EF 70-200mm f/2,8L IS II USM
What do you recommend?
Some general considerations - The Canon EF 100-400mm f/4.5-5.6 L IS USM Lens is best suited for wildlife and sports because it is reasonably fast, sharp, and accurate, but has the very wide range of 100-400mm. This allows you to quickly switch between subjects near and far, without switching bodies or lenses. This is an older lens in the lineup, as such its IS does not quite perform up to the standards of the newest lenses, but overall this a fair value for the price they are currently asking for it.
The Canon EF 70-200mm f/2.8L IS II USM Telephoto Zoom Lens is at the high end of the price range, as such it provides excellent image quality, maximum aperture capabilities, and image stabilization. This is an excellent lens for portrait photography, almost a requirement for indoor portraits for most professionals. This would be my pick out of the zoom lenses you mentioned, but it also demands the highest price. You could look at the still excellent version one of this lens to save a bit of money.
The Canon EF 70-300mm f/4-5.6 L IS USM Lens fits between the previously mentioned two lenses. It doesn't have quite the range of the 100-400, or quite the aperture of the 70-200, but it is kind of a best of both worlds. It is the middle of the road for weight as well. One consideration is weight, this is not as heavy as the 100-400, but not as light as some of the 70-200 options(especially non IS). This lens has excellent 4 stop IS and a great deal of newer features that the 100-400 simply does not offer.
Overall, the Canon EF 70-200mm f/2.8 IS II USM is probably the best lens of this range generally speaking. It also has the highest price. If you want to stay within your price range, consider the Mk I version or the non IS version. If you add a teleconverter to this lens, it turns into a fantastic sports and wildlife lens as well, so that pretty much covers all of the lenses mentioned here.
From your selection above, the 70-200mm f/2.8 IS II USM without a doubt.
It will take extenders excellently giving you additional zoom ranges, is incredibly sharp, has the latest IS, has a fixed maximum aperture and it covers a very useful range without extenders.
The 100-400 is a good lens (there are poor models out there which aren't as sharp as others) but they suffer noticeably when the light is poor (I have had one for 4 years). The trombone style zooming can be a bit cumbersome and I am about to send mine back to Canon for another repair to the zoom ring lock (although to be fair I have REALLY used it for 4 years and the first time I had an issue was earlier this year). I am planning to sell mine soon for a 70-200 f/2.8 non IS model.
70-300mm f/4-5.6 L IS - A new lens so it has all modern technology but the variable aperture would bug me at the price. You cannot fit extenders to this lens making it somewhat inflexible.
Agree with @dpollitt on most of these issues but have different reasons. First, I have all three lenses so I'm actually speaking about this from a "what I grab first" perspective.
The 100-400mm is the lens I use least. I probably would have opted for a faster 400mm prime if I had it to do over again because there is so much overlap with the other lenses. It's cumbersome and heavy and I'm not getting the aperture I want in exchange for that weight. In my opinion, even though a lot of nature and wildlife photographers swear by this lens, I find it not to be fast enough for sports or long enough for far away nature shots. An extender makes the speed issue worse and causes autofocus to become seldom-focus.
The 70-300mm is heavy but has incredible reach if you are looking to reduce the number of lenses you carry. I'm not a fan of this lens for reasons @dpollitt stated, but there are days when I just can't pack an extra lens and know I'll need an extra 100mm for some shots.
By far the most versatile of all the lenses mentioned is the 70-200mm, which is in heavy use all the time. It works great for everything from portraits to fashion to nature to architecture (!). There are a couple of lenses I use more, but only a couple. This is the one I would recommend you get if you are looking for an L series moderate tele-zoom. As far as the quality of the glass, it is sharp enough for the most demanding work.
Just to throw an extra choice in there, the 70-200 f4 L can be picked up well within budget and it's a beauty of a lens to work with.