Pushing has far less control because the center of mass is ahead of the applied force and any eccentricity in the applied force causes rotation in a direction other than that in which the force is applied.

On the other hand, pulling a cart means that the cart will rotate toward the direction of the applied force and follow it. The direction of a pulled cart tends to be self correcting (all things being equal).

It's also easier to get it over bumps, since you're pulling upwards, rather than pushing down into the ground. I'm not 100% sure that applies so strongly to the chinese design though.