300 F4 1.4TC vs 100-400
If you need lens for birding I vote for 400mm, it is very sharp wide open, and has very fast AF (faster than 100-400 or 300 f/4 + 1.4 TC), and handles wonderfully. f/5.6 is not very fast aperture for a 400mm lens, so you will probably shoot wide open almost all the time, prime is sharper wide open than 100-400 or 300 f/4 + 1.4 TC.
here is my experience with it:
You are welcome to have a look at my gallery: