From AikidoFaqs web pages:
"One of the other big breaks in Aikido history occured during O Sensei's life when Kenji Tomiki proposed "rationalizing" Aikido training using Kata and Competition. Since that time, there has been little commonality between the Tomiki schools and the mainline Aikido schools."
"In addition, he [Tomiki] believed that introducing an element of competition would serve to sharpen and focus the practice since it was no longer tested in real combat. This latter view was the cause of a split with O Sensei who firmly believed that there was no place for competition in Aikido training."
"Tomiki wished to obtain the blessings of the founder for his efforts. Exchanges of views took place between Tomiki and the Aikikai with Shigenobu Okumura often acting as intermediary. However, the founder was very firm on this issue and adamantly insisted that aikido did not include competition. A rift between Tomiki and the Aikikai consequently developed and Tomiki continued on his own."
"There is no competition in Aikido because it would eliminate a lot of people from the training. The purpose of Aikido is to allow as many different people as possible - men and women, young and old, weak and strong - to develop their potential through practice together." (Chiba sensei)
so it seems that it may have been an informal disagreement between Tomiki and Ueshiba. There is a brief section on Tomiki's approach to competition at:
Also, while I was trawling these pages I found an amazing story about Ueshiba which I'm not sure whether to believe - have a read yourself!
Sorry I can't help any further,