For me, when you consider a super tele, whether it be the FA 600/4, the DA 560/5.6 or the Sigma APO 500/4.5 there are two important factors that determine the real usefulness in the field.
these are Minimum focusing distance and weight. the difference of 1 stop at maximum aperture is somewhat marginal, for the lens on its own, but i admit that if you wish to add a 1.4x TC, this could be something that would make you exclude the DA560.
Lets look at the 3 lenses to see how they stack up.
FA 600/4, MFD = 5 meters weight = 6.83 kilos
DA 560/5.6 , MFD = 5.6 meters weight = 3.04 kilos
Sigma APO 500/4.5 , MFD = 4 meters weight = 3.15 kilos
For me, considering hand holding capability, either the DA560 or the sigma 500 come up equal. i can imagine holding either of these to get a shot, considering my present 70-200/2.8 plus 2x TC weighs in at about 2 kilos. Adding an additional kilo, is not all that bad, but adding an additional almost 5 kilos to go to the FA 600 is out of the question.
What would push me towards the Sigma over the DFA560 are the close focus, because i can see for small birds etc, getting 1.6 meters closer is possible, and also the additional speed to allow a 1.4x TC.
As for the absolute speed, I think that the low light/high ISO capabilities, since at least the release of the K5, have eliminated the absolute need for a super fast tele.
the following shot, i believe illustrates this point (ISO 6400 on the K5)
and by the way, this is a non cropped shot, so yes, i was pretty close
this is a JPEG right out of the camera, and it looks much better with simple sharpening, contrast boost and noise reduction, but I prefer to just show the JPEG here as a starting point. who reall needs F4 at 600mm