Nikon J1 vs Sony NEX 5
I had an NEX-3, and now have a Nikon V1. The NEX has better ultimate image quality, but was too slow to keep up with our toddler. The V1 is great for photographing kids. You will have to take it out of auto-everything mode to get the best results, but as long as you understand when to use single-shot or continuous autofocus, use center-point focus, and adjust ISO manually in dim lighting, you can get great results. Even with the relatively slow kit lens, I've gotten some great shots indoors without a flash. Shooting at 5fps and just keeping the best shots is pretty handy.
As a bonus, the Nikon 1 cameras take excellent videos with fast, continuous auto-focus. It's the first still camera that I've had that can replace a camcorder for me.