Just to be clear - I was referring to this class of questions as vulgar not you or anyone who asks them. It might be a fine line (I asked therefore I am) but it was not meant as such.
Is Karate better than Aikido?
Is Saito better than Tomiki?
Is Superman better than Batman?
There are just so many variables and at their respective pinnacles they themselves would not engage in such a contest. Well maybe Superman and Batman would but Batman (while having a way cooler car) would be an idiot for trying.
As I understand it after the initial meeting at a Daito-ryu seminar in Engaru at the Hisada Inn. Ueshiba later invited Takeda to Shirataki and they trained at the local inn. Again no challenges and by that time the student teacher relationship was already established. Try
for more detail of the first meeting and the early relationship.
Cromwell can you provide a source for the challenge match if possible. I really am curious.
By the by - the returning student you mentioned sounds like he learned his lessons in Iwama well. Too often people go and train at a Honbu for a relatively short time and just don't get it. Back in their own countries some act as if they are God's gift. He should be complemented.