Coinbase does not provide private key to users when using their wallet (Not vault). This can be insecure as there is an central point of failure. If they happen to have an extended unplanned downtime, you would be having problems trying to access it.
I would suggest you not to use Coinbase as your primary wallet. Blockchain.info will be a better choice for browser-based wallet.
However, the best choice is Bitcoin Core if you have the resources to run. Check out Mycelium too if you have Android smartphone.
For a browser based wallet, Blockchain.info isn't a good choice at all. Blockchain.info have a long history [1][2][3] for being inconsistent with their security. Even though they supposedly don't store unencrypted private key in their database. The most recent one[4] being them not checking the transactions if they are valid. This can potentially open up an potential attack for merchants using their API.
[1]http://blog.blockchain.com/2014/12/08/blockchain-info-security-disclosure/
[2]http://blog.blockchain.com/2015/05/28/android-wallet-security-update/
[3]http://www.forbes.com/sites/thomasbrewster/2015/02/24/blockchain-and-darknet-hacks-lead-to-epic-bitcoin-losses/
[4]https://www.reddit.com/r/Bitcoin/comments/3frn1d/satoshis_coins_have_not_moved_blockchaininfo_is/