Especially when duck shooting ie low light situations and shooting on driven pheasant days ie very fast subjects on close to full zoom.
To shoot birds in flight, you'll want at least 1/800 s shutter, and preferably 1/1600 s. Personally, I find that 400mm f/5.6 is decent as long as there's a reasonable amount of light (ok under a canopy in daylight, struggles a bit at dusk or under canopy with overcast skies). However, there's another consideration - with a longer lens, or if you're close to your subject, I often need to stop down to f/6.3 or f/7.1 to get the whole bird in focus.
Here's an example from a cloudy day:
EOS 7D, EF 100-400mm f/4.5-5.6L
IS USM @ 400mm, 1/1600 s, f/6.3, ISO 1600
As you can see, with reasonable light and 1/1600 s, I still needed ISO 1600...but I also needed f/5.6 or narrower for DoF.
So, I think you'd be fine with the 70-300mm f/4-5.6L IS. Having said that, I have and love the 70-200mm f/2.8L