What is a better sports photography lens?

I was looking at the sigma 120-300 f2.8 and the sigma 50-500mm f4.5-5.6 witch one would be better for cricket and AFL photos.
i have a nikon d90 so the crop factor might be a problem on the 120-300mm and will the 50-500 take as good photos as the 120-300mm.
can you please help me or tell me another lens that be good for me.

A good 50-500 can rival the 120-300 in comparable settings. The 120-300 acts as a quick f2.8 lens when you shoot sports. Put on a 2x TC and you got a very decent wildlife lens.

I use a 300 mm f/2.8 to shoot football (American) all the time with a D300, no problem. The same with basketball.

Samples

The 50-500 is two stops slower at 500mm than the 300mm at f/2.8

The sigma 150-500mm might be a better option.though it really depends on the level of cricket you are shooting and there you are in the crowd… A 300mm lens might not be able to get you into the action…

and hopefully you need just the focal length, without the light sensitivity…

A 50-500 at that speed I wouldn't touch… It'll be hard to get any decent shots in low light. And 500 on a Nikon crop sensor equates to 750mm on a D90… Far too long for field sports IMO… I'd go with your first option and use a teleconverter if you need more focal length… I use a 300mm f/2.8 prime for ice hockey and football… Along with an 80-200 f/2.8 and for wide shots for close up action a 24-70mm f/2.8… Note that all these lenses have the ability to go wide aperture for low light and isolating the action.