We're paraphrasing here and I'm going by what I remember of my research, but, yes, George is correct. Most people just remember Ueshiba saying that there is no competition because there should be no opponent or that competition was not a good spiritual goal.
Off topic a bit, but there are different definitions for "competition". Ueshiba mostly talked about sport-type competition. But he wasn't referring to the type of "competition" that occurs between students trying to be better than each other, or the competition of being tested (for example, push tests).