I'm currently using a 400mm F5.6L and 60D for birds photography and I'm also consider changing to a FF (I'm thinking of 6D), so here is what I think at the moment.
The advantage of FF is better image quality, better high ISO performance and better low light AF (both 5D3 and 6D had better low light AF than current crop sensor DSLR on paper), but the disadvantage is "lesser reach". Also, with a crop sensor, you are using the center "sweet spot" of the lens image circle, so your image is relatively sharper across the entire image compare using a FF.
With a 1.4x TC on 5D3 or 6D (on paper, 6D had better low light AF at center AF point than 5D3, so hoping it'll get F8 AF), you get closer to the "reach" of a crop sensor, but with a 1.4x TC, your AF will be slower which is not good for birds photography... now, the question is how much slower?
So I'm waiting for the 7DII specification to be out before I decide. Hopefully, the 7DII will have better low light AF and 1 to 2 stop better high ISO performance than current model... if not, I might change to a FF if F8 AF is not that slow.
Just my $0.02.
Have a nice day.