Nikon - Canon
You will be pleased with any of the four cameras.
All of the cameras offer lenses with image stabilization.
It is built into the lens, not the camera body itself.
It is very helpful when photographing moving objects.
The only real difference is "features".
The D5200 and 700D have articulated LCD screens.
I would like to have that feature.
Choosing either Nikon or Canon goes back over 50 years.
Nikon owners say choose Nikon.
Canon owners say choose Canon
Which speaks well for both cameras.
Visit a store that has both models and see how they feel in your hands.
Choose the one that feels right to you.
You can leave them in Auto if that is what you want.
But there are times that you will achieve better results by using one the the manual modes.
I suggest you experiment with the manual features too.