Cloud is also Data centers just with a virtualization software above it but its more advanced than the conventional data centers.
We can distinguish both in the following terms:-
Data Center:- Buy new RAM stick & install (very hectic and tedious)
Cloud:- Stop server change the instance size and restart.
Data Center:- Buy expensive setup or rent them.
Cloud:- Pay as you use. Comparatively cheap.
Data Center:- If there is a situation of natural disaster then the server will go down.
Cloud:- Data is being backed up at three different graphical location such that no disturbance occurs even if one goes down.
Data Center:- Adding or removing a component is not an easy task.
Cloud:- Adding or removing can be done with just few clicks.
These are the basic benefits you get when you switch to cloud!