I think the huge difference in price tell you something. mechanically (speed of AF), built quality and optically, 70-200mm is superior from 70-300.
Although the D700 (one of the best sports camera right now with d3 and canon 1d mark iii), has high range iso, but I will recommend you to to use lower iso as possible.
Between 70-300mm and 70-200, there is around 2 stops difference (aperture). I think it will deteriorate the image quality especially details in low light condition for example indoor or night sport.
With big aperture of 2.8, you can also have a shallower depth of field effect.
However 200mm is quite short, especially if you shoot in full frame format.
I use crop factor camera of 1.6 (Canon 40D) and here are my experience:
For football and soccer, usually more than 200mm is necessary to capture close action.
for field hockey 70-200mm is good enough (because the field is smaller.
for indoor, like volleyball, basketball it is perfect especially in full frame mode.
I never shoot rugby but I assume you might need longer than 200mm to capture close action.
There are ways to overcome the shortness of 70-200mm which are:
1. Cropping the image, but you will lose some details.
2. Buying and extender to increase the telephoto range. (but lose 1 or 2 stops as a result - max aperture become f/4 or f/5.6).
I saw many professionals use 300mm f/2.8 prime lens for field sport, but well, that lens is expensive and also huge to carry around. You might lose many shots due to inflexibility of the focal length.
If you shoot mainly in outdoor daylight, I think 70-300mm will be pretty good because the AF tend to be a lot better in bright condition and also you have extra 100mm reach compared with d700.
But if you concerned about the highest quality possible, indoor/low light shooting and might want to do something else with the lens such as portraits, then 70-200mm is the most suitable for you.
Sigma 120-300 f/2.8
Sigma 100-300 f/4
I use Sigma 100-300 personally and i find it to be quite ideal for daytime soccer. Although it is a lil bit big and heavy, but I can still manage to handhold it. There are a tripod ring that come with the lens so you can mount it to monopod/tripod.