Kyber is different because it is built on the Ethereum blockchain, and actually trades out of the Ethereum wallet you have directly. With Bitshares you first have to send your EOS (for example) into a BTS wallet, which then 'converts' your EOS into BitEOS (or OpenEOS if you come from OpenLedger) which is sort of like an IOU on the Bitshares network for an EOS token. Then when you want to take money out, it unwraps the BitEOSand gives you back the EOS.
With Kyber no such conversion takes place. Your EOS token is directly moved from your wallet into the buyer's wallet, and vice versa.
Kyber however currently only supports Ethereum based tokens, whereas Bitshares has Bitcoin and other blockchains, and even digitized/tokenized assets like Gold or other metals.