I actually just sold my 300mm F/4. That thing was terrible. It was extremely slow focusing and was not very sharp from 200mm on. Could be because it was an older model, but I have found my 55-200 to be pretty great in sports situations, but only in daylight. At night it was awful, I had to bump the ISO up to 1000 which gave me noise that couldn't be fixed. I am hoping the noise level is better on the D300s too, the D80 is horrible anywhere after 640.
You must've had a bad copy of the Nikkor 300mm f/4. Mine is very responsive with AF and very sharp IQ. Curious as to your statement that it is not sharp beyond 200mm. It is a fixed focal length of 300mm. 200mm is not applicable.
The 55-200mm is a consumer grade lens. It can take sharp images given enough light, but low light situations will show its short comings.
The D80 ISO performance suffers north of ISO800. I went from D80 > D300 > D700. I gave the D80 to my son but still have the other two. The D300(s) should suit your needs for sport photography and low light, but you'll still want to couple it with good glass to optimize its performance.