In my opinion, "hand-holdability" is not really an advantage in such long focal length. Both in sport and wildlife, you need to wait till the right moment to take the photo. Often, it can be a long wait !
Monopod or tripod allows you to get the best of the lens without pain !!

Choosing between the 400/2.8 and the 500/4 depends on your shooting ability and also the camera body you are using. Shooting with a 400mm at f/2.8 on a dense sensor can be very challenging and often requires specific skills (especially on fast moving subject), as the DOF is very shallow and the tiny pixels needs much better focus accuracy than large-pixels sensor.
Your need for converters (especially 2x TC) must be taken into account too when making your decision : in general a TCx2 works better on a f/2.8 telelens than a f/4 one, in particular when you use a high resulution body like the 7D.

Hope this can help you and good luck on your choice !