I'm assuming if there is dumping on both chains it would counteract each other. When the value of one chain drops, the value of the other would rise I would imagine. Although I'm unsure of how prices will react. Will the value of BTC instantly split into 2? Instead of having 1 coin valued at around $1000, you know have 2 coins (1 on each chain) valued at $500? It will definitely be a crazy ride seeing what will happen.
Not easy to predict price, but , after an initial chaotic period, it will tend towards a balance where the relative price is proportional to total hashing power on each chain.
There are a number of reasons that this happens, which include reflexive feedback loops from traders.