From Kybernetwork FAQ ;
What is the main difference in approach towards token convertibility between KyberNetwork and 0x Project? 0x utilizes offline channels to match makers and takers, but KyberNetwork matches and processes the order on-chain immediately. 0x's approach is to bring the order book off-chain and then execute the settlement on-chain. On the other hand, KyberNetwork's main proposition is to support on-chain and instant trades with guaranteed liquidity.
In order words, both order settlement and matching happens on chain. It seems to me that Kyber is more similar to Bancor with their instant liquidity pools, but as opposed to Bancor, the reserves are administrated by Reserve Managers, which monitor and determine prices. With 0x, orders are created and matched offchain by relayers, which is faster and cheaper than on-chain order-books & matching protocol. In addition, instead of having large reserves like in Bancor or Kyber, 0x is more oriented with having orders matched between buyers and sellers. Of course, in 0x a relayer could also act as a taker (seller) at the same time and maintain a huge liquidity pool, similar to what a Reserve Manager does in Kyber.