Hey Ali, I dont shoot that much sports in Low Light, but we do cover a ton of Musical Acts which is pretty much the same thing. I'm guessing Jana would be the one to ask about this as she covers a ton of sports and has quite the portfolio
The simpliest thing to recommend is a good, fast lens that will allow the shooter to stop down to an f/2.8 or lower. My ideal set-up is a Canon 70-200L IS f/2.8. The Image Stabilization on the lens really helps with the low light and the speed of the lens at f/2.8 is amazing. I've captured some stunning images with this lens paired up to numerous Canon bodies.
I'd love to test out the Sony stuff, but cant afford to try any of it out to see how it compares to Canon's stuff.
For Football in particular, if you have access to the sidelines and can move up and down the field with the play, a 70-200 lens will get you pretty tight in the action of the game. If you dont have access to the sidelines, then you're probably going to have to move up to a 300-400 f/2.8 prime lens. Either of these lenses are top notch pieces of glass and is what you see along the sidelines of 99% of the pro sports events anyway.
A camera body that can handle high ISO settings will really help with the shots too. Once the sun sets and the stadium lights come on, you're going to have to bump up your ISO till you can find that happy medium that will allow you to keep a fast shutter speed to stop the action. Blurry images in sports arent sold or looked for all that much, unless you've already captured the shot and are just looking for something artistic.
Here are a few shots taken with f/2.8 lenses in low light conditions to show you what they're capable of

Taken by my wife Cindy Bonish with a Canon 30D and the 70-200 IS f/2.8 lens I mentioned earlier
ISO400 1/125th @ f/2.8
Rock Bottom Chuck Wagon Rodeo in Arkansas 2009

Taken by Me, with a Canon 5D and a 400 IS f/2.8 lens on a Wimberly Head
ISO3200 1/250th @ f/2.8
Rock Bottom Chuck Wagon Rodeo in Arkansas 2009

Taken by Me, with a Canon 30D and the 70-200 IS f/2.8
ISO800 1/60th @ f/2.8
Red Bull Last Man Standing in Bulcher Texas 2007

Taken by Me with a Canon 30D and the 70-200 IS f/2.8
ISO640 1/125th @ f/2.8
Flint Michigan Ice Races 2009

Taken by Me with a Canon 1D and the 70-200 IS f/2.8
ISO800 1/100th @ f/3.2??? Not sure why I didnt open up to f/2.8, I must have had a few too many pops and wasnt paying attention to my settings
Mid-Eviel Times in Orlando Florida 2007
Hope that helps and I would bet to say that everyone will agree that a fast f/2.8 lens will be your best bet for low light sports photography.