One more reason that I prefer Panasonic - Panasonic lenses are optimized for video and have silent autofocus motors. Sony (and most Canon and Nikon) lenses are optimized for still photography and have noisy autofocus motors. Please listen to the lens motor in this A57 autofocus test. Great autofocus, but noisy motor:
Sorry for the multiple posts, but the forum only allows one video per post.
My bottom line recommendation for high quality stills and video of children with autofocus that works, 1080/60p, no moire, no limits on video clip length, no lens motor sounds on your soundtrack (if it fits your budget) is the $750
Panasonic DMC-G6 when they become available in the US in June.
This will be the best still/video camera below $1000 (I have the
Panasonic GH3, but this camera is $1300 body only).
My second choice would be the
Sony A57 for its fast, accurate autofocus and smooth 1080/60p frame rate.
A distant third is the
Nikon D5200 for its lack of moire (but the autofocus struggles and it lacks 1080/60p)
I would avoid Canon DSLRs for this purpose. They are fine still cameras, and pretty good for narrative video - but they are not very good family video cameras.
All the best - and good luck with your decision
Bill
Hybrid Camera Revolution