I will throw my 2 cents into this discussion since I have used the 300f4 with and without TC, the 400 5.6, and the 100-400 extensively.
The 300 f4 is a great lens by itself but it is a bit short most of the time. That is annoying. When a TC is put on it the sharpness drops to about the same as the typical 100-400 but the AF is slower. It has a short min focus distance of about 6 feet.
The 400 5.6 is fantastic for sharpness wide open. It allows fast shutter speeds with lower ISO than the 100-400L and if youre always at 400 then this is the clear choice. Its is slightly sharper than a decent copy of the 100-400L. It has a longer min focus distance than either the 300 or 400 (12ft)
Now for the 100-400L, which I own and shoot with all the time. It is a great lens if you want a one lens does it all deal. It is sharp wide open (but not as sharp as the prime). It is about the same weight as the 300 and 400 primes. It has IS that is usable but not fantastic. If you think it doesnt work, just turn it off and look through the viewfinder and watch the subject move all around, turn it on and watch the subject sit still.
The AF is very fast if you flip the focus limiter to 6m-infinity, but its plenty fast at 1,8m - infinity.
The 100-400L has a short min focus distance (6 ft) for when you get really close to things.
I prefer a zoom, no question about it. While MOST of my shots are at 400mm I find enough of my shots are below 400mm that I would not want to give up that range for the small sharpness increase with a 400mm prime.
Here are a few examples with my 100-400L. Please check my flicker for more. Almost every shot on there is with the 100-400L. If you dig deep you will find a few with the 300 and 400 primes but you cant tell the difference between them and my 100-400.
Coyote before sunrise by jhayesvw, on Flickr
IMAGE LINK: http://www.flickr.com/photos/jhayesvw/10386844535/
Black Throated Sparrow on Ocotillo by jhayesvw, on Flickr
IMAGE LINK: http://www.flickr.com/photos/jhayesvw/9703471664/
Western Diamondback Rattlesnake by jhayesvw, on Flickr
100mm. Lizards are easy to get close to.
IMAGE LINK: http://www.flickr.com/photos/jhayesvw/9367813742/
Short Horned Lizard by jhayesvw, on Flickr
THis one is with the 400 5.6 in perfect light.
IMAGE LINK: http://www.flickr.com/photos/jhayesvw/9100514023/
Getting Low Burrowing Owl by jhayesvw, on Flickr
This one is with the 100-400L. with a worse background and farther distance at the same place and time.
IMAGE LINK: http://www.flickr.com/photos/jhayesvw/9100516287/
Burrowing Owls by jhayesvw, on Flickr
Gila Monster at 130mm. Again, lizards are easy to get close to in the wild.
IMAGE LINK: http://www.flickr.com/photos/jhayesvw/8629277992/
Gila Monster by jhayesvw, on Flickr
I have hundreds more, check my flickr.