I think it depends on what you are doing.  Eventbrite is good if you are charging for an event.  LinkedIn could be good depending on who your audience is.  One thing that I do find frustrating about Facebook Events is that you can’t directly invite all your Fans.  

What have others experiences been with Facebook Events?

I love Facebook events!!
We just used both Eventbrite and Facebook events for our towns New Years Eve street party and we had waaaayyyy better results with FB !  By that I mean I was able to interact and answer questions of potential guests (we live in a town of 50k) 
  It was a ticketed event I had Eventbrite ticket form plugin on the event – we didn’t sell 1 ticket via Eventbrite but several hundred via Pay Pal on our website – which of course we linked to in the description on our Facebook event.   I have used it to promote a raffle we have had in our ice cream store (made the event dates be the entire time you could enter the raffle so it stayed on the ‘events’ list for people and that got some good buzz. 
   @social butterfly – I do not believe that is possible but if I hear of anything I will let you know. 
   For weekly events (car cruise night, etc) we don’t create an event because there is no ‘recurring’ option with Facebook and just use the pages wall to post reminders. 
  You can even take out an ad for an event – works great too!
 Here is my thought – People are already using Facebook daily, why try to get them to go somewhere else, come to them with your Event in the place they already are!! 
  Best of luck and let me know if I can help in any other way Eden