A shutdown is a complete power down of the system. When started again, its a fresh load of the OS and the related services.
Hibernation is typically a process where the OS will take it's current state (memory, running apps, etc..) and write the state to a file on the Hard Drive then power down. When the machine is started again, the OS will take the hibernation file and reload the contents so that you can continue on from the exact same point.
Yes, I agree with Abraham. Hibernating is usually better as it saves your time when you want to work again, without taking much time to close all your files and shut down, and then restart and open all your files when you're ready to work again.
Both are may some different
When you Shutdown all process of your computer is stop means your computer like dead.
While Hibernate your PC means your PC save the last all session of your data it take some 1.0 GB occupy for that then close unnecessary process and some process are running.Hibernet is like PC is shutdown but all data will be stored on Drive when you again start it will recover all data and you get as when you close computer.