Nikkor or sigma lens?

I shoot with a Nikon d80 but am soon getting the Nikon d3s. I'm in the market for a new lens, and I'm wondering which brand is better, nikkor or sigma. I'm trying to decide between the nikkor 80-400mm, the sigma 80-400mm, or the sigma 120-400mm. I mainly do sports photography (I shoot at equestrian events), therefore I need a fast shutter. Which do you think is best?

Nikkor

Nikkor, even though I guess Sigma is cheaper…

Nikon glass will almost undoubtedly be better than Sigma glass. Also, consider prime lenses, like the 300mm F4, which will allow you to get a faster shutter speed than a zoom.

Shooting with a fast shutter will require you to have a fast aperture. Though I can't specifically say which is better because you supplied no links. Do you mean the f/4-5.6? Or the f/2.8? I almost ALWAYS favor the camera brand as far as lenses, in this case Nikkor. I would simply go with whichever one has the fastest aperture, and is best within your price range. Typically I use http://www.bhphotovideo.com/...video.com/ for all my lens shopping because it has loads of information on each of the lenses, and buyers can put reviews.
With telephoto lenses I try and stay away from slower apertures like f/5.6 because it will force you to use slower shutter speeds and higher ISO, risking the quality of your images. If you can shell out a grand or two, I'd buy the f/2.8 in any situation.

Although every mainstream manufacturer makes good and not so good models in their range, I would tend to go with the Nikkor lens. They will almost certainly cost more, but your glass is arguably the most important piece of kit. Put inferior glass (and I'm NOT saying Sigma is) on the most expensive camera and you will probably never be happy with the results. As you are spending big money on the body, it would be a let down to cut corners on the opticals as it will probably not do the camera (and your pictures) justice by getting the best out of them.

If you can, get to handle both lenses, compare prices and do not be afraid to angle for a discount if buying on the high street. Of course, there's an art to this, but it is your money to spend where you want eg.online or elsewhere.

Oh yes, remember to buy a lens for a full frame camera, not a DX size sensor. I know you can shoot in DX format, but with a full size sensor that would be a waste of resource.

I just like to add that the 80-400 update is hitting the rumor mill. I wouldn't be surprised on it's replacement in 2011. The 80-400 was the first VR lens in Nikon's line-up and is a bit long in the tooth. I have heard of decent things with the Sigma 120-400 though, so it's worth a look.

In order for you to get a fast shutter speed, you need to have fast glass. Yes, I know you can crank up your ISO, but the Depth of Field difference between f/5.6 and f/2.8 is huge. You simply can't isolate your subjects at f/5.6 as you would at f/2.8.

At $5200, the D3s is a huge jump. How about getting a D700, Battery Grip and install the D3s battery (with adapter) into the grip? You should get around 8fps. Take the extra $2000 and put it towards glass, such as the Nikon 300mm f/2.8 with a Tele Converter? Just throwing it out there.