I found this at another site, thought it would be of interest
Both lenses are excellent and produce great imagery as do all that family of lenses. Don't be fooled into thinking about selecting any of the four 70-200mm "L" cousins due to image quality differences - there is just not enough difference between the four lenses to consider IQ as a selection parameter.
The primary differences between the f/4L IS lens and the f/2.8 IS are maximum aperture and size + weight.
The extra stop of the f/2.8L MAY allow you to stop subjects at a lower light level however, often the single f/stop is not quite enough to make a difference in hand held photography.
I can shoot my f/4L IS at 200mm lens at 1/60 second and expect to achieve near 100% sharp imagery and I can even shoot at 1/30 second and expect a high degree of sharp imagery.
I realize that IS will not stop moving imagery. However, I could not expect anyway near 100% sharp images if I were shooting with the f/2.8 non-IS lens at 1/120 second and would probably get no sharp imagery if I shot at 1/60 second. These two speeds would be the f/2.8 equivalent of 1/60 and 1/30 second at f/4. Sure, IS will not stop moving subjects but, if the entire image is not sharp - the subject will not be sharp. Additionally, using the IS Mode II, I can often get good panning shots of a moving subject at a speed at which I could get no sharpness without IS.
Yes, you can use a tripod or monopod with the 70-200mm f/2.8 and take advantage of the extra f/stop over the f/4L. However, when I am shooting sports, I will normally use the 70-200mm hand held and have a longer lens on a monopod. The 70-200mm is fine when the action draws closer but, does not have enough reach for mid-field shots.
The f/2.8 lens can provide a shorter depth of field which can isolate players but, using 200mm and f/4, the depth of field is reasonably short. A 200mm lens at f/4 focused at 20 feet will provide a depth of field of less than six inches with a 1.6x camera. Using a full frame camera, the DOF is about 8.5 inches. At 40 feet the 1.6x f/4 DOF is 21 inches. This is, IMO, plenty short to isolate individual players.
Some posters make much of the fact that the f/2.8 lens can be used with a 2x TC and still focus with 1.6x cameras. This is a non-factor to me since I don't think much of the results of using a 2x TC.
I shoot with the 70-200mm f/4L IS and 300mm f/4L IS lenses which suits me just fine. But, if I were shooting professionally, equipment cost would be no problem and I would use a pair of 1.3x cameras with the 70-200mm f/2.8 IS lens hand held and the 400mm f/2.8L on a tripod.
The reason that I did not select the 70-200mm f/2.8L non-IS lens is not the image quality nor the price - both the f/4L IS and the f/2.8L non-IS are pretty equal in those areas.
I chose the f/4L IS because it is a far lighter and smaller sized lens than the f/2.8L. I use my f/4L IS lens as half of a two-camera/two-lens package along with the 17-55mm f/2.8 IS lens for all of my travel and general purpose photography. I can carry the f/4L IS lens and a 40D camera at just about the same weight as the f/2.8L alone. I carry the f/4L IS everywhere and never leave it home due to its weight, This is very important to me as is the ability to hand hold my 70-200mm f/4L IS lens in lower light levels than I could the f/2.8L.
The lighter weight and better hand holding capability makes my f/4L IS lens a far more versatile tool in the way I shoot with it.
Let me modify my statement to say probably the best tele zoom from Canon currently is the 70-200 f/4L IS. That is supported by various reviews and MTF data. My bet is the mkII f/2.8 evens that out completely.