The basic difference between datacenter and cloud is that in datacenter you can store your data in hardware which can be located in your building and can be used in your local network. Using cloud allows you to store your data on the Internet.
Choosing between cloud and datacenter depends on how your company is. If you want your data to be customizable and not going to be handled by a third party then datacenter will be suitable. But you will not have unlimited capacity of storing data. Thats why people use Cloud because you can increase your data storage capacity. But it will be handled by a third party. So choosing between these two depends on what kind of business you are running, budget and how you want to handle privacy.