I chose the f/4L IS
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.