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One big difference is 0x is a protocol and is designed such that others build upon it. There will ultimately be many 0x relayers which will push down fees and increase liquidity. Kyber relies on reserves of tokens to execute trades instantaneously where as 0x relayers simply match up buyers and sellers.

You can google "kyber vs 0x" and read more about it, but at this point neither have a working product so comparing them is tricky. It is safe to assume whoever can execute trades fastest for the lowest fees with the highest liquidity will win in the long run. 0x will be first to market with the earliest relayers launching over the next 1-2 months, so we'll see how it goes from there.