Hey there Syazanie Amirin,
Below is a bit of overview, and my thoughts on the two methods, in case it helps.
Local storage lets you save and load specific data, and importantly, when you load data, you can use it whenever an however you want.
The save system saves a complete snapshot of the entire game state. Loading a state is kind of like time-traveling back to exactly how things were when the state was saved.
Save system exemption
There are lots of situations where you may not want the entire game restored that way, because some information about progress you may want to keep. (e.g. Unlockable items.) To avoid losing that information, you can exempt certain objects from being captured by the save system using the "No Save" behavior.
But if this information is saved by the save system, then how do you avoid losing it when you close the game? Well, this is another situation where local storage can help. Anything data that should persist between play sessions, that isn't getting saved by the native save system can be manually saved to local storage.
Save system quirks
Finally, the native save system is quite good, but there's one quirk that can cause problems. It may not save absolutely everything exactly as it was, and this can cause some problems when restoring. The only example of this I've found is that you can selectively disable collisions between different Physics objects, but when restoring from a save state, that disabled-collision-state information is not restored.
I wrote up a bug report for this issue at the link below.
The game I'm working on uses Physics objects with some disabled collisions, as a result I don't use the save system at all, and rely exclusively on local storage.
This is just my experience with the two methods though. Hope this helps.