I get this question a lot from those who are shooting with SLR video cameras, they are struggling with focusing during video recording and think something may be broken when in actuality, its more a matter of sensor size.
We know that there are 3 basic rules to DOF:
1. Aperture Size
3. Focal Length of your Lens
A forth and critical rule is the physical size of the recording media:
The Larger the Media, the more shallow the depth of field.
Because the Canon 5Dii has a HUGE sensor, the DOF will be more shallow all things being equal when compared to a 1.6 Sensor or a typical video camera. A very small sensor size allows for a very deep DOF, which means there is much more room for error when focusing on a moving subject.An additional problem is that the SLR camera has to rely on the usual (photography) focusing system for video. In the first models, this was somewhat of a nightmare, because you had to flip the mirror down to do this (blocking off live view), but improvements are allowing for new ways to focus in video, with the mirror up. Its getting better with each model, and will continue to improve.
I guess what I am saying is this: If you have very young children and intend to use a video SLR hybrid camera to record them, you will need to be extremely proficient with your focusing skills to get anything usable (especially if they are in the running around uncontrollably stage of their lives).