We haven't done it ourselves, but have seen them as they take place at the same time as the Character Tea - if dining with characters is your thing - go for it, the CMs will bring out your cake and sing Happy Birthday and you get a present, don't know what though.
We've done the Character Tea twice, obviously because of the characters it is popular for young children, so expect to have a lot of children present at the meal.
This thread tells you what food to expect Plaza Gardens Character Tea
Birthday Party booked. Was surprised at the very casual attitude of the CM, he was pleasant enough but only gave me a reservation number when I asked for it. It seems the times have changed to 3.30 and 5.00. He never asked the age of the birthday girl, I guess 40 may have shocked him