These three articles lay out the rationale behind Ethereum Classic using SHA3:

(1) Introduces ECIP-1049 and the proposal itself.

https://medium.com/@antsankov/ecip-1049-why-ethereum-classic-should-adopt-keccak256-for-its-proof-of-work-algorithm-e45aee32d8a9

(2) Why SHA3 is better algo than Ethash.

https://medium.com/@antsankov/pt-2-ecip-1049-why-ethereum-classic-should-adopt-keccak256-for-its-proof-of-work-algorithm-24052ea6eed1

(3) Mining you Internet Connection. Why SHA3 mining on ETC will be different than SHA256 on Bitcoin.

https://medium.com/@antsankov/pt-3-ecip-1049-mining-your-internet-connection-why-ethereum-classic-should-adopt-sha3-71ac74a94868