I did have blockchain as my first wallet but 1 day I had a deposit of 0.0168 from someonei didn't know then the next day someone else sole that and about $2 I had in there. I did only havea good password on that wallet as protection so probably my fault but I just found coinbase easy to use and I like the security they offer.
I use multibit 4 cold storage just because I found a YouTube video on it and a friend also advised me that is been safe 4 him.
All web based bitcoin services (Coinbase, blockchain.info, etc) will be insecure if you have malware running on your computer (key logger, trojan, browser plug-in, etc). This is because when you log in, the malware can capture the information that is returned to your browser and use it to impersonate you.
Also, if you don't use 2FA and you use a weak password, then your Coinbase account will be just as insecure as your blockchain.info wallet was.
You'll have to decide for yourself which service you prefer.
With Coinbase, you are giving your bitcoins to the company. They are no longer "your" bitcoins. Insead the bitcoins belong to Coinbase. They have complete control over the bitcoins, and you can't do anything with the bitcoins without their permission. Coinbase promises to keep track of how many bitcoins you've given them, and they agree to allow you to make requests to spend/send that same amount of their bitcoins to anywhere you want. When you log in, you see an "account" where they tell you how many of their bitcoins they are still allowing you access to. When you spend/send bitcoins somewhere, you are sending a request to their servers asking them to send their bitcoins there, and then waiting for their software to create the transaction and send the bitcoins for you. Since you don't have sole control of the private keys, you can't access the bitcoins if they experience technical problems (denial of service attack, crashed servers, business shut down, filed bankruptcy, etc). You are trusting the company to handle backups and offline storage properly for you. If you forget your password, it is possible to get it re-set and to restore your access to your account.
With blockchain.info, you maintain sole control of your bitcoins. The company is unable to access or spend the bitcoins. You are responsible for your own backups and cold storage. As long as you maintain proper backups, you can still access your bitcoins if they experience technical problems (denial of service attack, crashed servers, business shut down, filed bankruptcy, etc). Since your password is used to encrypt the private keys, it is impossible to re-set a lost/forgotten password. If you forget your password, your bitcoins are permanently lost.