Of the two lenses your comparing, the 70-200mm F4 L is definately the better quality and faster lens. I've read of many Canon users really liking this one. So, despite it not being stabilised; it may be the better choice for you.
It does rather depend upon what you intend to do with it! If it's for Airshows etc, then you need more reach. So, the 70-300mm would offer that. However, you may do better fitting a 1.4 convertor to the 70-200mm F4 and getting the extra reach that way. 200mm x 1.6 = 320mm x 1.4 = 448mm (35mm equivalent).
All that said, most Canonists at Airshows migrate to the 100-400mm Zoom it would appear.
I'd go and check with the Canon forums at
www.dpreview.com