In regards to the whole Dr. Kawashima vs. Dr. Lobe debate:
The official website for Big Brain Academy actually cites Brain Age as the game that started the educational game trend. Thus, Dr. Kawashima comes first. Big Brain Academy was different from Brain Age because the training exercises looked like games and because there was a strong emphasis on multiplayer.
That being said, it's unlikely that Sakurai would get the Doctor's permission to appear in the game. Also, the Doctor has appeared on other systems, making him less of a "Nintendo" all-star. Therefore, I'm not sure that he would make it in.
Dr. Lobe doesn't have the popularity, but he still has moveset potential from his two games. I own both Big Brain Academy series, but I don't have any of the Brain Age games, so I have a bigger attachment to him.
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Now I have an urge to make a Dr. Lobe thread.