As the victim of losing most of my crypto to Mintpal and now blockchain.info's horrible security over the past few months, I am now a security-minded first person, which is why I ask.
It has advantages and disadvantages compared to an exchange.
On the plus side, the server does not normally have access to your spend key so your coins can't be stolen if the exchange is hacked (or claims to have been hacked). On the negative side, you are typing (or pasting) in your seed words every time you log in, and those provide full access to your coins so any kind of malware on your computer could intercept that. Also, legitimate exchanges normally keep most of their coins in cold storage so even in the event of a hack, only a portion would be lost. (Poloniex was hacked, lost some coins, but was able to recover and eventually paid everyone back.)
Used carefully from a very secure computer (and only from the computer) the web wallet should be safe. A very secure computer is not necessarily easy to set up and maintain though.
