Bitfinex was founded in December 2012 as a peer-to-peer Bitcoin exchange, offering digital asset trading services to users around the world. Bitfinex initially started as a P2P margin lending platform for Bitcoin and later added support for more cryptocurrencies.
In 2015 the exchange's customers were hacked, losing about $400,000, and in 2016 about $73 million more was stolen from its customers' accounts. [source]
Coinbase was founded in June 2012 by Brian Armstrong and Fred Ehrsam. Coinbase is a digital currency exchange headquartered in San Francisco, California. They broker exchanges of Bitcoin, Bitcoin Cash, Ethereum, Ripple, Zcash, Dash, Monero, Litecoin and other cryptocurrencies with fiat currencies in approximately 32 countries, and bitcoin transactions and storage in 190 countries worldwide. [source]