Once you have established small circle push-hands there are lots of subtler games that can be played from it.
Big Circle push-hands gets it's name because to play it one must break the small circle. The rule set allows for grabbing (chin na), plucking (zai), elbow strikes, throws, and traps (zhou), forward strikes with the shoulder (kao), and two directional attacks to the opponent's frame which can be light swipes, slaps or sudden jolts(lieh).
Most people learn both big circle and small circle at the same time. I think that is a mistake, the two rule sets should be clearly differentiated. The question remains, which is better to learn first?
Small Circle push-hands is the heart of the game, but to deal with an aggressor you must know Big Circle push-hands cold.