Well, let’s make a comparison:
Over 97 percent of coins are kept in cold storage. The private keys used for authorization of cold storage transactions are held in fragments between offline hard drives and paper, in different locations with backups in case of losing any pieces.
They offer two-factor authentication for logins and withdrawals and allow customization for maximum daily transaction limit. Passwords are hashed and encrypted.
They offer email notifications and use PGP email encryption. The exchange hasn’t been hacked in the past.
In the aftermath of the Mt. Gox colapse, Kraken was the first company to create a cryptographically verified proof of reserves which shows that the exchange holds 100% of customer funds, as it should. They hold the majority of funds offline in a cold storage. Their servers are held in secure facilities with armed guards, retina scanners and top-notch video surveillance.
The company has two factor authentication, PGP encryption for email communication and a global setting lock, which prevents any account changes in a certain time period.
So far, Kraken hasn’t been hacked, but there were cases where careless users got their accounts hacked due to lack of 2fa security.
These two exchange platforms offer the most robust security in the entire Bitcoin exchange market. In terms of security – your funds would be safe on both of them.
However, when we consider all other aspects – Kraken is a better choice than Coinbase. Coinbase is known for violating users’ privacy, tricking their affiliate associates and taking sides in BTC debates (exchanges should remain neutral). There are numerous complaints online about these issues, so I would go with the Kraken.