The 70-300 I believe would be a better choice. It's a better optical performer, it has a much better build and has some useful features such as a manual focus override function, a focusing window, and as you mentioned the better AF.
You could also look at a few other lenses that may suit you well. There's the 70-200 f/2.8, which although it is more expensive and you lose 100mm, it opticially blows the 70-300 and 55-300 out of the water, and offers a much faster aperture. There's also the 300mm f/4 prime, which is priced in between the 70-300 and 70-200, is very sharp (considering that it's a prime lens) and gives you an extra 100mm over the 70-200 and an extra stop of brightness over the 70-300. There's also of course the 300mm f/2.8, but unless you have $5000 to throw around, I couldn't recommend it.
What's your budget on this lens?
-Evan