Sorry, I don't have suitable comparison shots right now but you're really looking at two very different lenses with different design aims.
The 28-300L is a general do all lens aimed at togs who need quick flexibility....always having the right lens on. I have the forerunner of this, the 35-350L, and sharpness and focus speed is much slower than the 70-200L's. Achieving end to end sharpness for a 10x plus zoom is is always going to be a challenge.
The 70-200 on the other hand is sharp and responsive...easy to achieve with a 3x zoom but may fall a little short for motorsports without the addition of a T/C (I have the IS version)
I'm not trying to put you off either lens...they both have there place and are good within their design criteria but I find it hard to end up a with a scenario that both could be considered for.
Bob