All cameras, even $60 point-and-shoot models, have a fast enough shutter speed to freeze motion. That is not the issue. The issue is understanding exposure and knowing how to use the camera.
The T4i is a more capable camera, but that doesn't necessarily mean it is a better camera. The capability comes at the expense of size, weight, and more complexity as a system. Of course you can use the Canon in fully automatic mode, but you won't get the maximum from the camera by relying on the camera to make all the decisions for you.
The NEX-6 is very small, especially with the power zoom kit lens. Technically speaking, it has a more modern sensor than the T4i. If you intend to use either camera mostly in auto mode, the Sony has its much more advanced Intelligent and Superior Auto modes. But if and when you decide you need different lenses, flash options, audio, remote control, etc., it's a poorer choice, because it is more limited as in system components (although non-native lenses can be used with adapters, but then you start to give away size and ease of use).
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