I don't know that I'd call the cloud more or less secure than stuff stored outside of the cloud. Maybe "differently secure", with a slight hint of "less secure". (I almost hate myself when I talk like that.)
You look at a cloud, and what you see is a hopefully strongly secured data center that's putting check (or "tick") marks in all the right boxes...strongly secured facilities, a responsive attitude to pushing out security fixes and encouragement to use good security practices.
But...that's not all of it. A data center from a big name like Amazon or Google can't help also being a big target...anyone planning a physical, legal or "vigilante" (think DDoS attack) attack on one of those has a fairly large target to hit, and the odds (at least so far) of their being successful have been demonstrated to be pretty good (at least for DDoS, which is usually effective enough).
You also don't know how old disks and servers are being handled when they are removed from service...was your data properly scrubbed off of these devices, if it was ever written in cleartext to start with? What about employees working for the cloud provider, even ones that are just doing their jobs?
Software security issues must also be considered. When your service faces something as large as the Internet, many people are trying to pry it open and look at things they shouldn't.
In that vein, I think there is greater security to be had in, say, Unexpected Bill's "little" computer installation, mainly because it's not a big name service. I don't have man traps and 24 hour cameras or a security service, but who cares about the piddly little amount of computing I've got going on? Someone might steal my computers on general principle, possibly to fence or strip them for components, but they probably wouldn't be very interested in the contents of them. I also know what I'm doing when I retire old equipment, and I'm in control of how my data is secured when it is being stored. I also know what I'm doing to make backups, and how to test them.
Don't get me wrong--I don't think the cloud is useless. It does have its merits. Whether or not it can be made into a satisfactory solution for those who demand the ultimate in security...I don't know. It's plenty good enough for "a lot" of things.