The post above is extremely useful (great find
@BlackHorsePhotos ). Looking at the FX corner (far right), the bare 600 seems much sharper to me than the 400 with tc engaged. The center is also slightly sharper, but very slightly. If the primary use is wildlife photography, then corners usually don't matter so far that use the 400 plus tc may be fine. I wouldn't want to use it for architecture, but then again I don't know anyone who does architecture photography at 560mm!
I think the deciding factor is if you sometimes need to shoot at the shorter 400mm setting and/or in low light where you need f2.8 . If so, then the 400 TC seems like a logical choice (if I wanted a super tele that is what I would get just for the 2.8 ). However if you shoot almost exlusively at or near 600mm then it makes little sense to buy a shorter lens with the intention of keeping the teleconverter engaged full time.