My online wallet is blockchain.info. I have last 3years but never had any problem from it, I never use coinbase.com because has many restrictions. . coinbase.com blocked my account because I deposited from the casino,
Coinbase is an exchange company so expect some restrictions like that, blockchain on the other hand is purely a web wallet. Also they are dealing with buy and sell bitcoin options aside from other services they are offering. Basically they are an active company performing what a company must supposed to do invloving money. How can they faced the laws they are under now if they will not have at least some information of their clients. About the blocking issue, they really told you that your account was blocked because you deposited from a casino?
But you know if that kind of thing is really out of your line then it's fine if you will not use it anymore.