Not sure if I've ever had birch beer. Are we talking alcoholic stuff or regular? I never knew that there were alcoholic versions of Root Beer or Birch Beer until reading the Wiki articles.
When I was a little kid, Root Beer tasted like nectar from the Gods to me. My older Bros. first job was at a Dog and Suds. We went to pick him up one night after closing and all the teen employees were having a root beer fight. I was absolutely stunned - I couldn't imagine how people could waste such a rare and delicious substance.