How do you guys record your kids' sports? Disclaimer - my wife is not only camera illiterate, she doesn't want to know (yeah, worse case). I'm hoping the 70d would be super simple for her to use.
If I read correctly, you're interested in autofocus capabilities. I own this camera for ~2 weeks now, and I played a little with it. I use it with a 17-55 IS USM.
You can either use Servo AF (full automatic) in video mode (either with face tracking or simply a certain point), or you can turn it off and use focus by hand.
When using Servo AF, it zooms slower, more gradient, but accurate, no hunting. This is good for overall usage, and can track anything moving at "normal" speed. This cannot track very fast movements like full zoomed on a kid's face who's running around. But for wide, it's working perfectly. I read in a Canon paper that the engineers slowed down the focus change to have movie look, because it can perform much faster (see next option).
The other option is to turn Servo AF off and use manual autofocus. It means that the camera focuses to the place where the focus box is when you push the AF-ON button. This is very fast, almost instantly, no hunting. Not as fast as the conventional PDAF AF, but almost at fast, always < 1sec, usually ~0.5 secs. This is good when you're moving the camera and when you stand on a new object, push the button, and it gets focus. Also, in this mode, the focusing noise of the lens is only heard when you push the button.
My lens has an audible noise, mainly in Servo AF where the camera is always focusing. in AF-ON mode, its better because much infrequent. According to the reviews, STM lenses have no audible noise and they focus smoothly.
So, if you like to record games, not fully zoomed on faces, I think you'll be satisfied with the Servo AF with an STM lens. 55-250 STM is now available, try one because it has the coverage I think you need.
The sensitivity of the sensor is a bit better, but it doesn't matter for outdoor sports. Compared to the 5d3, you don't have Tv and Av modes on this camera, only AUTO and MANUAL. In AUTO, you cannot set ISO, in MANUAL, you need to set everything manually (but there is auto ISO). So, in MANUAL, you set the aperture to the desired, you set the shutter speed to 50 and you set auto ISO, it'll work fine.