If you are using a Desktop, Sleep mode will be a better option. Both Sleep & Hibernation mode help in saving energy. However, with Sleep mode, booting is a bit faster. Let's see how.
When we shut down the PC, it closes all the running programs and operating system. When we start the PC, it starts up afresh from the clean state and runs only those programs that were scheduled to run on start up. We need reopen the files etc, we were working on before the shut-down. This obviously takes time.
With Sleep Mode, the PC cuts the power from all the modules of PC except from the RAM. That's because the RAM contains all the program data from applications we were running before we had put the PC to sleep. But this means constant power supply is needed for RAM. That's why Sleep mode is good for Desktops, with power from Wall outlets. When we start the PC again, it starts from where we left i.e., all the files and process are saved.
But with Laptops we do not have the luxury of constant power supply. So, we use Hibernate mode. In this mode, first of all, the data in RAM is written into the hard-disk and then power from all the modules of laptop, including RAM, is cut off and no more power is required. When we start the Laptop, the data is written back from hard-disk to the RAM and laptop starts from where we left.
Since in Hibernate mode, data needs to be written to and fro from RAM and hard-disk, Hibernate mode is comparatively slower than the Sleep mode.
However, it should be kept in mind that these modes are better used for saving the power and not as an option to increase boot speed. A proper shut-down/restart will still be required.
In order to improve start-up, I would suggest to run "msconfig" utility in WINDOWS and deselect the unimportant programs, so that they do not consume time and memory at startup.
Hope this helps!!