I agree with others who say IQ is probably not the deciding factor here. You're considering two great lenses, both of which are capable of producing outstanding images. One is f2.8, the other is not. You're not a professional photographer, you're someone who wants great images of your kid doing sports.
Do you need f2.8? Will you use it, or will you stop down the lens? Is f2.8 capability worth the considerable extra weight?
You're going to use the lens to photograph your son's soccer games. Is this the only thing you'll use it for, or will you also want it for other activities with your children, such as trips to the zoo, outings to the park, parties, school events, etc.? If you're going to use the lens for other family activities, the weight should absolutely be a consideration.
Speaking as someone who's been in your shoes, chose a heavy lens and eventually sold it for a lighter one (because I hated carrying it and didn't like shooting with a monopod), I'd strongly suggest renting the Sigma first, to see if you actually enjoy using a large, heavy lens. This will make your decision a lot easier.
If it helps, I had a similar dilemma to yours: I owned a much-loved 70-200 f4 IS that was a bit too short for the sport I enjoy shooting. Having previously tried the experience, I knew I didn't want a heavy lens and I knew I could live without f2.8 capability. I chose the 70-300L and have absolutely no regrets - none. As Ed Rader pointed out, it's small and compact enough to take everywhere, the AF is second to none, and the images it produces are outstanding. On paper it doesn't look like much: but in real life it's a terrific piece of equipment.