The main difference is the Sony uses the mirrorless concept.
That makes for a smaller/lighter camera due to the digital viewfinder.
But smaller also means the battery is also smaller (less shots per charge cycle).
However if you plan to use manual focus, the optical viewfinder on the Canon is better suited for manual focus.
The Sony is twice as fast when in continuous mode (10 shots per second).
For video, the Canon has a microphone jack so that you can use an external microphone.
And you need a better microphone on either camera.
I am looking at the Sony NEX 6 and the T4i. I have used cannons my whole life so I feel like I know them but would consider my self a cannon pro.
All I want is to take photos of babies and family, I want to be able to capture the moments. Which camera would you recommend?