Definitely the 70-200mm f/4L IS. I carry mine everywhere and shoot it in tandem with a 17-55mm f/2.8 IS lens on a pair of 1.6x bodies. The reasons I chose the f/4L IS over the f/2.8L non-IS are:
1. Weight: I can carry the 70-200mm f/4L IS PLUS an additional 1.6x camera for the weight of the f/2.8L alone.
2. The extra stop of the f/2.8L lens is not a magic panacea for lower light shoooting. I can shoot my f/4L IS hand-held when cranked out to 200mm at 1/60 second and expect perfectly sharp imagery. I could not shoot the f/2.8L at 1/120 second and expect 100% sharp imagery. I can shoot the f/4L IS at 1/30 second and still get a reasonable percentage of keepers. I could get NO keepers shooting the f/2.8L at 1/60 second.
3. Even in sports, I would rather have an overall sharp image with my subject blurred a bit than an all over unsharp image. Additionally, the extra f/stop will often not make the difference between a sharp and a motion blurred image.
4. Some photographers detract from the f/4L IS because you cannot shoot with a 2x TC on a 1.6x camera and retain auto focus. However, I don't like the results from the 2x TC. It may be satisfactory for some photographers but, not for me.
5. Much is said about DOF at f/2.8 and how it can isolate subjects. However, I quite often shoot at f/4 and get a narrow DOF, especially at closer focusing distances. Additionally, the f/2.8 DOF at 200mm can frequently be too narrow.
6. However, I would not choose the f/4L IS because it is supposed to have better IQ than the f/2.8L. Both lenses produce magnificent IQ and I don't think you could pick out, based on IQ, from a series of photos shot with all the five 70-200mm cousins which image was shot with which lens.
BTW: I own the f/4L IS, have previously owned the f/4L. I can use my IS version 4-5x more often than the non-IS model. The non-IS f/4L is not, IMO an all-around lens like its sibling the f/4L IS. I have shot with the f/2.8L and did not like its size and weight.