Autofocus during video is still an important feature. That, and continuous autofocus with moving subjects, have been problem areas for Micro Four Thirds. High end DSLR cameras handle continuous autofocus, e.g., for sports and wildlife, very good. This is due to using PDAF technology. Micro Four Thirds cameras, with the exception of the Olympus E-M1 so far, only use CDAF, not PDAF.
Achieving efficient autofocus during video with CDAF is a matter of having fast image processing capabilites, combined with good algorithms for interpreting the data. GH3, being the newest and most powerful of the GH-line, of course has the best potential here.
Here is a video comparison of the GH2 and GH3 both doing AF with the Sigma 30mm f/2.8 DN lens mounted. The Sigma 30mm f/2.8 is a reasonably compact, inexpensive and very good lens. Read about how the test was done below.
Both cameras were mounted to a Desmond Mini Dual Camera Bracket, typically used for stereo photography. On the lenses, I have used 46mm to 28mm step down rings as hoods. They do a good job of keeping the front lens elements safe from accidents, in my opinion, while also keeping out some stray light. If you want to use them, you also need a 28mm front lens cap.
The GH3 was set to 1080p, 50fps. The shutter speed was 1/60s, which should be fairly safe to use, given the lens's 60mm equivalent field of view. For a true 180 degree shutter, perhaps 1/100s would be a better shutter speed.
With the GH2 I used 1080i, 50fps. Sadly, the GH2 is not capable of progressive video at 1080 rows and 50fps. I still chose to use 50fps, since a higher framerate typically gives better AF during video. I also set the shutter speed to 1/60s with the GH2.
I was surprised to see that the GH3 did not clearly outperform the GH2. That is what I saw previously, when comparing the cameras with the Lumix G 14mm f/2.5 mounted. Perhaps the GH3 is optimized for use with Panasonic brand lenses, and cannot to the same extent excel when using third party lenses like the Sigma 30mm f/2.8 lens?
All in all, the GH3 probably comes out on top in this test, but not by a big margin. This shows that continuous autofocus is still the Achilles' heel of the Micro Four Thirds system. The Olympus E-M1 pro camera does implement PDAF, however, it is not used during video recording for better focus accuracy.
The Nikon 1 system is so far the only mirrorless system that implements PDAF successfully during video recording. There is also the Sony SLT system, which uses a non-moving semi-transparent mirror for PDAF focusing, and can focus quite effectively during video recording. The downside, though, is that the camera and the lenses are bulky due to the longer register distance.
In interviews, Panasonic representatives have said that they don't believe in PDAF for their mirrorless camera systems. This is in contrast with almost all other manufacturers, who appear to be launching cameras with PDAF these days, e.g., Canon EOS 70D, Fujifilm X100S, and Sony A7.
Rather, Panasonic appears to think that CDAF will be sufficient for the task, by increasing the processing power and improving the AF algorithms. And in my test using the Lumix G 14mm lens, it worked impressively well. In this test with the Sigma 30mm lens, though, I was a bit disappointed. We still need more development from Panasonic in this area.