Sleep uses the battery a bit.
The advantage is it resumes where you left off and is fast to start using.
The disadvantage is you can loose unsaved work if the battery goes flat or something goes wrong during resume. Also if the battery goes flat when it is sleeping you cant use it when you want to without a power source.
(Note: it is possible for a sleeping notebook in a carry bag to overheat and be damaged)
Hibernate does not use the battery.
The advantage is it resumes where you left off and is fast to start using, but not as fast as sleep.
The disadvantage is if something goes wrong during resume then you can loose unsaved work.
Shutdown uses no battery
The advantage is the computer starts afresh so can be more responsive compared to a computer that hasn't been shutdown or restarted for a few days.
The disadvantage is it takes time to boot, and if you forget to save work it is gone for sure.
Hope this helped