Several good options here.
I own both the original EF 70-200mm f/2.8L IS USM as well as the version "II" (currently that lens is about $1900). The differences are:
1) The version II has improved the optics. This almost suggests the optics in the I weren't good... in fact they are great. The difference doesn't jump out at you, you really have to pixel-peep to notice the improvement.
2) The version II has improved the speed of auto-focus.
3) The version II has improved the Image Stabilization system. This means when you're shooting 4 stops below the minimum recommended shutter speed for hand-held photography without image stabilization, the II will be more likely to get a "keeper" than the I. IS doesn't "guarantee" you can shoot at low speed and still have no blur from camera motion... it just skews the odds for you to make the probability of getting a "keeper" to be more likely. The II would have a better "keeper" rate than the I.
One caution about IS ... the IS system only helps eliminate blur caused by CAMERA movement. It does not help eliminate blur caused by SUBJECT movement. Since you're shooting action photography, you'll still need fast shutter speeds to deal with the subject movement.
Both of these lenses have something that really stands out in the industry -- they're NOT "heavy breathers". Most other lenses in their range actually are heavy breathers. That means that if you zoom to the 200mm end you'd think you actually have a 200mm lens. On a "heavy breather" you'd only really be at 200mm if you focus to infinity. Focus closer to minimum focusing distance for the lens and the focal length drops dramatically (a heavy breathing 70-200mm lens set to 200mm but focused to minimum focus distance usually *actually* has a focal length down in the 130-150mm range (no kidding!)). These Canon lenses actually stay within 5%... meaning at 200mm and minimum focus distance they are still providing 190mm -- which his extremely good performance for a lens.
200mm isn't a lot of focal length when shooting subjects 100 meters away. For that, you might prefer something in the 300-400mm range.
The Canon EF 100-400mm f/4.5-5.6L IS USM II is a fantastic performing lens (about $2000)... but remember that this is a variable focal ratio lens where the f-stop can drop to as low as f/5.6 when zoomed to the 400mm lens (meaning it's getting 1/4 as much light as the 200mm f/2.8). You would have absolutely no problem in mid-day and evening... but at dusk you might start wishing you had an f/2.8 lens.
Another possibility is to pair the 70-200mm lens with a 1.4x or 2x extender. The 1.4x converts a 70-200mm f/2.8 lens into a 98-280mm f/4. The 2x converts it into a 140-400mm f/5.6. But usually there is a slight overall loss in sharpness when you add an extender into the optical path (there is no free lunch). You probably should go look for some sample images because while what I said is technically true, there are lots of examples where photographers get extremely good results.