I wouldn't consider comparing both lenses wide open a fair comparison, one is f/2.8 while the other is f/4-5.6. If you compare them at similar apertures then they are more or less the same, both winning and losing at different focal lengths. Both are sharp lenses and both can be used professionally.
The main differece is going to be your use and personal preferance. If you do a lot of low light with moving subjects or portriats the the 70-200mm f/2.8 is going to be a much better choice, and the f/2.8 aperture is going to give a brighter viewfinder and faster, more acurate and more AF points because of the f/2.8 aperture. If this is a walk in the park/landscape lens then the 70-300mm is a better choice. Lighter weight is also a plus, although I personally don't consider that a big deal.
Edit.
Just a side note, why not consider a used 70-200mm f/2.8 IS original version? It's about the same price as either lens and has the fast aperture and IS, you will be able to shoot in much lower light levels with the fast aperture and IS. This would be my first choice.
John.
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