I'll chime in with another recommendation for the Canon 70-300mm L. My copy is tack sharp at all focal lengths, and really shines at 70mm and 300mm - even wide open. I've used and compared my 70-300mm L with various 70-200mm Ls and eg Sigma telezooms (except the Canon 70-200mm f2.8 II), and my 70-300mm L is as sharp as any of the others (eg a good 70-200mm L f/4), and sharper than most (eg 70-200mm f2.8 IS mk I). Some copies of the f2.8 mk II might be a tad sharper, as Neuroanatomist points out, and as he says - it's not much (critical pixel peeping level, I expect).
The weight, balance, accurate & fast AF, great IS, build quality and range of focal length are what convinced me to buy and keep the 70-300mm L. And as has been pointed out in thejoyofsobe's post - it retains its aperture at a decent rate (eg still f5.0 till 228mm!) Of course f2.8 is more glass, letting in more light, but you pay by lens weight. Anyway, I consider truly 'fast' f1.8 or more.
Maui5150, I hope that you will make a purchase that meets your needs and that you'll capture many good photos with it. As you indicated, the difference in price between the 70-200mm L f4 and 70-300mm L f4-5.6 is only $230, which I really agree isn't much for the extra mm you're getting!