Both would be very adequate cameras, and you could have a great experience whichever way you go, but I will throw in a few caveats.
In order to do sports photography, there are 3 things which are usually recommended: 1) fast shutter speed, 2) good ISO performance (especially for indoors or evening photography), and 3) fast auto-focus. Neither of those options come for cheap.
The professionals would recommend either the 500mm f/4L IS USM for daylight, or the 300m or 400mm f/2.8L IS USM for night / indoors. All of those options are in the 5000$-10000$ range with a high-end camera body such as the 1D X, which has insane ISO performance, amazing fps, and crazy auto-focus. In order to freeze the action, you will need a fast shutter speed. In order to have a fast shutter speed at night time or indoors, you need to play with the ISO and the aperture of your lens. If you make sacrifices on either the camera body or the lens, you will have a harder time taking pictures. Not to say you won't take some amazing ones, but your % of good shots will be lower than using the top gear, especially for sports photography.
If you had another main interest, such as portraits, I'd say a T2i with a 50mm f/1.8 and a Nissin 622 flash would be plenty to get you started. But sports photography is another beast where more $$$ = better shots (at least if you know how to handle that expensive gear).
A good compromise would be the T4i which can be pre-ordered now. It comes with 9 cross AF-points, and can shoot 5 fps. The low-light performance should be improved over the T3i, so an improvement on all 3 essential sports requirements. I would expect up to ISO 1600 shouldn't be a problem (as opposed to ISO 800 for T2i/T3i), and ISO 3200 should be doable on a stretch. Anything higher would be only good for newspaper or personal use.
Another caveat is the lens. Unless you would be taking photos right on the field, chances are you'll need some sort of telephoto lens. The Tamron SP 70-300mm VC USD would be the minimum I would recommend for this, coming in at 300$-500$ depending on your location. A 70-200mm f/2.8 would be another great option also, giving you better aperture so you can use a faster shutter speed, but losing on some distance.
Cameras: Canon EOS 6D, Canon EOS Rebel T3i, Canon EOS Rebel T2i, Canon S90
Lenses: Tamron: SP 24-70mm F/2.8 Di VC USD, SP 70-300mm F/4-5.6 Di VC USD, Rokinon: 8mm Fisheye cine, Canon: EF-S 18-55mm f/3.5-5.6 IS Lens, 75-300mm f/4.0-5.6 III, and EF 50mm f/1.8 II
Retired camera: Fujifilm Finepix s700