Something I have found...
I was having the same problem, I think, with my S3.
When I entered an event into my Google calendar, it would quickly appear on my droid calendar.
When I entered an event into my droid calendar, it would not appear on my Google calendar.
Recently, my calendars would sync without problems but something stopped that from happening.
I spent time with Sprint, to no avail, but found something that actually worked...But first, ten annoying minutes of commercials! (Just kidding)
When you add an event into your droid, near the top of the screen is the entry which allows you to select which calendar it goes to. If it says "My Calendar", you're outta luck. Change it to your Google account and it will work beautifully.