I know the online exchanges keep the private keys in "cold storage"-- so it comes down to can the average person keep the private keys safer than the professional corporations with huge amount of resources? In addition if there is a security breach, it seems like there would be a better chance of you coming out whole if your funds were on an exchange.
Definitely, however the answer is for most people probably not. It requires discipline to actually secure your assets, but you could effectively make it 99% sure that your assets are safe with a offline wallet. Something which banks can't do. Banks have an issue with cyber attacks, as well as actual physical attacks, and being a public bank they actively broadcast they have a lot of money in their vaults.
As for exchange being breached, then history tells us that usually the customers are the ones to get hurt. You'll probably find it in their terms of service that they aren't responsible for any data or funds breaches. The fact is; the attack vector on banks, and exchanges are much larger than Billy Joe down the street who owns a couple of Bitcoin. Malicious users will always go for the biggest target, since they have more chance of actually coming out with something.
It's exactly why Microsoft Windows operating systems are targeted more by malicious code than Linux, though that changes when you get into servers. Though, most low level criminals are targeting the every day user, because it's the easy of the two.