Ethereum Classic (ETC) is not an original cryptocurrency, but rather the older version of Ethereum (ETH). It all began with the DAO fiasco in 2016 and the need to bring changes in the Ethereum blockchain, leading to a hard fork. The people who were against the hard fork supported the original Ethereum, which was later renamed Ethereum Classic, and the upgraded version or the hard forked version, (ETH) Ethereum.

Ethereum Classic is an open-source, decentralised blockchain technology platform possessing smart contract functionality. Much like Ethereum's blockchain, Ethereum Classic's blockchain is quite similar too, with the exception emerging from block 1920000. Also, Ethereum Classic uses the proof of work protocol instead of proof of stake, which is used by Ethereum and many other cryptos.

Ethereum Classic -

Pros

 Stays true with the philosophy of the immutability of the blockchain.
 Has recently got the backing of a few big players

Cons

 Doesn’t get access to all the new updates made in the ETH chain (for instance the change from Proof of Work to Proof of Stake protocol).
 All the influentials of the Ethereum have moved on to ETH.

Ethereum -

Pros

 Is growing at an exponential pace.
 Has the majority of the original influentials who have created Ethereum.
 Has reversed the DAO hack and given back the stolen money to its rightful owners (the DAO token holders).
 Is being constantly updated with the latest changes.
 Has a higher hash-rate than ETC.
 A powerful example of what the Ethereum community is capable of when it comes together to solve a problem.
 ETH is backed by a powerful group of over 200 corporations called the Enterprise Ethereum Alliance (EEA) which aims to use the blockchain technology to run smart contracts at Fortune 500 companies. Members include Microsoft, JP Morgan, Toyota, ING, etc.

Cons

 Goes against the policy of immutability.