I tried that experiment, and the first couple of years it was about 50/50, but most recently almost everyone who posted did so on the FB birthday date. I think theyv'e come to rely on the Facebook reminders.
It was also interesting to see the cognitive dissonance from some posts: "I'm pretty sure it was your birthday next week, but Facebook says its this week, so Happy Birthday".
Of my friends who are friends but not best friends, I only know one of their birthdays. I only know that because her Xbox Live gamertag has her birth month and day in it (and she was born one year and one month before me, kind of interesting I guess).
Birthdays are a thing that are hard to remember. People used to mark them down on a calendar or just wait for the person to remind them. Both of those functions have been replaced with Facebook now.
It was also interesting to see the cognitive dissonance from some posts: "I'm pretty sure it was your birthday next week, but Facebook says its this week, so Happy Birthday".