Here's some examples of Sony DSLT's AF:
Continuous AF in video, tracking moving cars
http://www.youtube.com/watch?v=_qoVCBFnQzY
You will notice that, due to phase AF, there is no hunting when the subject moves and the camera refocuses.
AF speed:
http://www.youtube.com/watch?v=b9nLcv6hLsQ
This video is to show the AF refocusing speed when the camera needs to quickly refocus.
Do note that the lenses used in the above 2 videos are non motorised lenses, thus their AF speed is not that fast (not the fault of the camera, its the lenses). Sony has motorised lenses (termed SSM), and those lenses are MUCH faster than their normal lenses.
Also, the A33 and A55 are Sony's entry level DSLRs. Sony will be coming out with their semi pro DSLRs later this year, and its AF speed (in video and in photo shooting) will be even faster than the entry level A33/A55.
You can compare it against the
Nikon D3100's video mode, which uses contrast detection (and this is one of the fastest contrast detection AF in video in the market right now)
http://www.youtube.com/watch?v=0pOJ1eikUeQ
You'll notice that everytime the D3100 needs to refocus, the front back focusing hunting occurs. Also, most times the camera needs to stop moving for a little while, before the camera will try to focus. And whats worse is the "rubberband effect" (look at 1:28 - 1:30min, at the fences, when the camera is moving).
The front back focusing of contrast detection is very annoying in video...