As soon as you say "BIF", the 400f5.6 should really be first in line.
The 400f5.6 is also very light for what you get. Basically you cannot do better if straight "BIF" is what you are after.
From what I've seen I have no desire to trade up my 400f5.6, plus if you stick a 1.4xTC on that thing the IQ blows every option below $7,000 out of the water (it just doesn't autofocus at the same time).
Now, in this case we're after "large BIF", and not just "BIF", so if the birds are more lumbering around than darting back and forth then maybe the autofocus isn't as important, and for many the 100-400 is good enough and the added flexibility is worthwhile.
If the subject is moving fast I say stick with the 400f5.6, if it's not the Tamron is probably the way to go.