The short answer is yes. First off, there's multiple types of cloud-based data centers that range from Tier 1, Tier 2, and Tier 3 data centers. The number represents the type of redundancy; so a Tier 3 data center is going to have three types of redundancy for the main areas of power, physical security, and internet connectivity.
Think of an extremely secure building from a physical standpoint with locks, doors, Biometrics, even fences around the cages and cabinets that hold the servers that represent your company. That's one area of security from a physical standpoint.
From a network data security standpoint, there's additional security built in to the routers, switches, firewalls, and security software that is typically more expensive and unobtainable for a small to medium-sized business from a cost standpoint.
Another aspect of security in the cloud would fall under redundancy. Each Cloud installation is typically residing on a set of three servers referred to as a cluster. So, if there are any hardware issues on one of the servers, the services automatically fail over to another server. So where yes, initially cloud services could look a little bit more expensive on a monthly basis, you're buying that redundancy in that fault tolerance that if you were to produce the same result in your own office, with your own hardware, you would then most likely have a higher expense.