I also own the Canon 70-300mm f/4-5.6L zoom and like it too, however, my preference for bird photography is the Canon 300mm f/4L prime over the zoom. Mostly since I like to have the option of using the 1.4x extender — ** the 70-300mm zoom does not allow an extender — physically / mechanically it won’t fit.
https://www.amazon.com/Canon-300mm-Telephoto-Fixed-Cameras/dp/B00009R6WW

